Maths-
General
Easy
Question
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-
- 5
- 21
- 38
- 8C3
Hint:
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Here we have to find the number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty.
The correct answer is: 21
A permutation is the non-replaceable selection of r items from a set of n items in which the order is important.

A combination is created by selecting r items from a group of n items without replacing them and without regard to their order.

Here we have given the word as: MISSISSIPPI.
Here we have to find the number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty. So:

I = 4 times,
S= 4 times,
P = 2 times,
M= 1 time
So the number of words will be:

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is 21.
Related Questions to study
physics-
A mass of
strikes the wall with speed
at an angle as shown in figure and it rebounds with the same speed. If the contact time is
, what is the force applied on the mass by the wall

Force = Rate of change of momentum
Initial momentum
Final momentum

Substituting
Force on the ball
Negative sign indicates direction of the force
Initial momentum
Final momentum
Substituting
Force on the ball
Negative sign indicates direction of the force
A mass of
strikes the wall with speed
at an angle as shown in figure and it rebounds with the same speed. If the contact time is
, what is the force applied on the mass by the wall

physics-General
Force = Rate of change of momentum
Initial momentum
Final momentum

Substituting
Force on the ball
Negative sign indicates direction of the force
Initial momentum
Final momentum
Substituting
Force on the ball
Negative sign indicates direction of the force
maths-
If the locus of the mid points of the chords of the ellipse
, drawn parallel to
is
then 
If the locus of the mid points of the chords of the ellipse
, drawn parallel to
is
then 
maths-General
Maths-
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-
If nCr denotes the number of combinations of n things taken r at a time, then the expression nCr+1 + nCr –1 + 2 × nCr equals-
Maths-General
maths-
The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -
The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -
maths-General
physics-
An intense stream of water of cross-sectional area
strikes a wall at an angle
with the normal to the wall and returns back elastically. If the density of water is
and its velocity is
,then the force exerted in the wall will be

Linear momentum of water striking per second to the wall
, similarly linear momentum of reflected water per second 

Now making components of momentum along
- axes and
-axes. Change in momentum of water per second


By definition of force, force exerted on the Wall

Now making components of momentum along
By definition of force, force exerted on the Wall
An intense stream of water of cross-sectional area
strikes a wall at an angle
with the normal to the wall and returns back elastically. If the density of water is
and its velocity is
,then the force exerted in the wall will be

physics-General
Linear momentum of water striking per second to the wall
, similarly linear momentum of reflected water per second 

Now making components of momentum along
- axes and
-axes. Change in momentum of water per second


By definition of force, force exerted on the Wall

Now making components of momentum along
By definition of force, force exerted on the Wall
physics-
The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line
will

When the length of spring is halved, its spring constant will becomes double

Slope of force displacement graph gives the spring constant
of spring
If
becomes double then slope of the graph increases
graph shifts towards force- axis
Slope of force displacement graph gives the spring constant
If
The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line
will

physics-General
When the length of spring is halved, its spring constant will becomes double

Slope of force displacement graph gives the spring constant
of spring
If
becomes double then slope of the graph increases
graph shifts towards force- axis
Slope of force displacement graph gives the spring constant
If
physics-
Two small particles of equal masses start moving in opposite directions from a point
in a horizontal circular orbit. Their tangential velocities are
and
, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
, these two particles will again reach the point 

Let initially particle
is moving in anticlockwise direction and
in clockwise direction
As the ratio of velocities of
and
particles are
, therefore ratio of their distance covered will be in the ratio of
. It means they collide at point B

After first collision at B, velocities of particles get interchanged,
.,
will move with
and particle
with 
Second collision will take place at point C. Again at this point velocities get interchanged and third collision take place at point A
So, after two collision these two particles will again reach the point A
As the ratio of velocities of

After first collision at B, velocities of particles get interchanged,
Second collision will take place at point C. Again at this point velocities get interchanged and third collision take place at point A
So, after two collision these two particles will again reach the point A
Two small particles of equal masses start moving in opposite directions from a point
in a horizontal circular orbit. Their tangential velocities are
and
, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
, these two particles will again reach the point 

physics-General
Let initially particle
is moving in anticlockwise direction and
in clockwise direction
As the ratio of velocities of
and
particles are
, therefore ratio of their distance covered will be in the ratio of
. It means they collide at point B

After first collision at B, velocities of particles get interchanged,
.,
will move with
and particle
with 
Second collision will take place at point C. Again at this point velocities get interchanged and third collision take place at point A
So, after two collision these two particles will again reach the point A
As the ratio of velocities of

After first collision at B, velocities of particles get interchanged,
Second collision will take place at point C. Again at this point velocities get interchanged and third collision take place at point A
So, after two collision these two particles will again reach the point A
maths-
In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is
In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is
maths-General
maths-
The number of non-negative integral solutions of x + y + z n, where n N is -
The number of non-negative integral solutions of x + y + z n, where n N is -
maths-General
maths-
Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -
Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -
maths-General
maths-
If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -
If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -
maths-General
Maths-
The number of numbers between 1 and 1010 which contain the digit 1 is -
The number of numbers between 1 and 1010 which contain the digit 1 is -
Maths-General
Maths-
The number of rectangles in the adjoining figure is –

The number of rectangles in the adjoining figure is –

Maths-General
chemistry-
Assertion :this equilibrium favours backward direction.
Reason :
is stronger base than 
Assertion :this equilibrium favours backward direction.
Reason :
is stronger base than 
chemistry-General
Physics-
A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at
is

Vertical component at
A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at
is

Physics-General
Vertical component at