Question
Eight chairs are numbered from 1 to 8. Two women and three men wish to occupy one chair each. First women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from the remaining. The number of possible arrangements is-
- 6C3 × 4C2
- 4P3 × 4P3
- 4C2 × 4P3
- None of these
Hint:
We will first start by using the method of selecting r objects out of n objects that is 
for finding the ways in which we can select two chairs for women and three for men. Then we will permute the men and women among themselves.
The correct answer is: None of these
DETAILED SOLUTION
Now, we have been given 8 chairs which are numbered from 1 to 8. Also, it has been given that women choose the chairs from amongst the chairs marked 1 to 4, and then men select from remaining chairs.
In total there are 2 women and three men who wish to occupy one chair each.
Now, we know the number of ways of selecting r objects among n is . So, we have the ways in which we can choose two chairs among four numbered 1 to 4 is 
and we can arrange the women then in 2! ways. Also, we have the ways of selecting 3 chairs among the rest 6 chairs is 
and in them we can permute the men in 3! ways.
So, in total we have number of possible arrangements as,
2! 
3!
Now, we know that = 
Therefore, we have,
Total ways = 
It is important to note that we have used a fact that = . This can be understood as we know that = 
and 
= 
. So, substituting this we have = .
Related Questions to study
A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?</span
Whenever we face such types of problems the key point is to make special arrangements for the people who are in need of it, then arrange the remaining. Now combination comes with permutation as there are possibilities of these 8 people sitting on one side to rearrange. Thus this concept into consideration, to get through the answer.
A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?</span
Whenever we face such types of problems the key point is to make special arrangements for the people who are in need of it, then arrange the remaining. Now combination comes with permutation as there are possibilities of these 8 people sitting on one side to rearrange. Thus this concept into consideration, to get through the answer.
If (m+n) P2 = 56 and m–nP2 = 12 then (m, n) equals-
If (m+n) P2 = 56 and m–nP2 = 12 then (m, n) equals-
A thin uniform annular disc (see figure) of mass 
has outer radius 
and inner radius 
. The work required to take a unit mass from point 
on its axis to infinity is
A thin uniform annular disc (see figure) of mass has outer radius and inner radius . The work required to take a unit mass from point on its axis to infinity is
The two bodies of mass 
and 
respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is
The two bodies of mass and respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is
If 
to 
terms, 
terms, 
, then 
If to terms, terms, , then
The coefficient of 
in 
is
The coefficient of in is
Compounds (A) and (B) are – 
Compounds (A) and (B) are –
A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:
A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:
is reciprocal of the one of the roots of equation 
then
and 
have a common root then 
is equal to
to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is
has the value equal to –
simplifies to
