In how many ways can $10$ identical presents be distributed among $6$ children so that each child gets at least one present?

Open in App

Solution

The number of ways of distributing $N$ identical objects among $R$ group such that each group can have any number of objects is given by:
$C (N + R - 1, R - 1) = C (10 + 6 - 1, 6 - 1)$
$= C (15, 5)$
$= 3003$

Suggest Corrections

Similar questions

Q. In how many ways

8

balls can be distributed among

3

children so that one child gets

4

balls and two children get

2

ball each?

Q. In how many ways

12

apples can be distributed among

4

children such that every child gets at least

2

apples?

In how many ways 15 chocolates can be distributed among 6 children such that everyone gets at least one chocolate and two particular children get equal chocolates and another three particular child gets equal chocolates.

Q. The number of ways in which 10 identical apples can be distributed among 6 children so that each child receives atleast one apple is

Q. In how many ways can 14 identical toys be distributed among three boys so that each one gets at least one toy and no two boys get equal number of toys.

Join BYJU'S Learning Program

In how many ways can 10 identical presents be distributed among 6 children so that each child gets at least one present?

The number of ways of distributing N identical objects among R group such that each group can have any number of objects is given by:C(N+R−1,R−1)=C(10+6−1,6−1)=C(15,5)=3003

In how many ways can $10$ identical presents be distributed among $6$ children so that each child gets at least one present?

The number of ways of distributing $N$ identical objects among $R$ group such that each group can have any number of objects is given by:
$C (N + R - 1, R - 1) = C (10 + 6 - 1, 6 - 1)$
$= C (15, 5)$
$= 3003$