Q. 1.17 - A First Course in Probability

Question

Seven different gifts are to be distributed among $10$ children. How many distinct results are possible if no child is to receive more than one gift?

Step-by-Step Solution

Answer

The possible number of distinct results are $604,800$.

Step 1. Given information.

No. of gifts $=7$

No. of children $=10$

No child is to receive more than one gift.

Step 2. Find the possible number of distinct results.

No. of children eligible for first gift $=10$

No. of children eligible for second gift $=9$

No. of children eligible for third gift $=8$

No. of children eligible for fourth gift $=7$

No. of children eligible for fifth gift $=6$

No. of children eligible for sixth gift $=5$

No. of children eligible for seventh gift $=4$

Therefore, the possible number of distinct results are $=10\times 9\times 8\times 7\times 6\times 5\times 4=604,800$.