Question
The number of ways in which three persons can dress themselves when they have 4 shirts. 5 pants and 6 hats between them, is
 ^{4}C_{3} × ^{5}C_{3} ×^{6}C_{3}
 ^{4}P_{3}×^{ 5 }P_{3} × ^{6 }P_{3}


Hint:
Here, we can use the formula
The correct answer is: ^{4}P_{3}×^{ 5 }P_{3} × ^{6 }P_{3}
Given that,
Shirts = 4 , Pants = 5 and Hats = 6, which are distributed among 3 men.
For shirts, Number of ways they can wear =
For pants, Number of ways they can wear =
For hats, number of ways they can wear =
Total number of ways they can wear
Thus, the number of ways in which three persons can dress themselves when they have 4 shirts. 5 pants and 6 hats between them, is .
Related Questions to study
Eleven animals of a circus have to be placed in eleven cages, one in each cage. If four of the cages are too small for six of the animals, the number of ways of caging the animals is
Eleven animals of a circus have to be placed in eleven cages, one in each cage. If four of the cages are too small for six of the animals, the number of ways of caging the animals is
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
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 = .
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
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 = .
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 ?
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 ?
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) }P_{2} = 56 and ^{m–n}P_{2} = 12 then (m, n) equals
If ^{(m+n) }P_{2} = 56 and ^{m–n}P_{2} = 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: