Home
Class 12
MATHS
A person tries to form as many different...

A person tries to form as many different parties as he can, out of his 20 friends. Each party should consist of the same number. How many friends should be invited at a time? In how many of these parties would the same friends be found?

Text Solution

Verified by Experts

Let the person invite r number of friends at a time. Then, the number of parties are `.^(20)C_(r)`, which is maximum, when r=10
If a particular friend will be found in p parties, then p is the number of combinations out of 20 in which this particular friend must be included. therefore, we have to select 9 more from 19 remaining friends.
hence, `p=.^(19)C_(9)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Mohan has 8 friends, in how many ways he invite one or more of them to dinner?

A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

A man has 10 friends, in how many ways he can invite one or more of them to a party?

A number of four different digits is formed with the help of the digits 1,2,3,4,5,6,7 in all possible ways. (i) How many such numbers can be formed? (ii) How many of these are even?

Seven relatives of a man comprises four ladies and three gentlemen: his wife has also seven relatives-three of them are ladies and four gentlemen. In how many ways fan they invite 3 ladies and 3 gentlemen at a dinner party so that there are three mans relatives and three wifes relatives?

A farmer has a field in the form of a parallelogram PQRS as shown in the figure. He took the mid- point A on RS and joined it to points P and Q. In how many parts of field is divided? What are the shapes of these parts ? The farmer wants to sow groundnuts which are equal to the sum of pulses and paddy. How should he sow? State reasons?

A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosed once. Find the probability of getting.

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in the party, is :

A fair coin is tossed four times and a person win R1 for each head and lose R1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of the amounts.