Question 93

Find the number of ways of distributing five identical chocolates and six identical cookies among three children so that each child gets at least one cookie.

The number of ways of distributing $$n$$ items among $$r$$ persons isΒ $$^{n+r-1}C_{r-1}$$

If at least one item is given to each person, then the number of ways isΒ $$^{n-1}C_{r-1}$$

As there are five chocolates and three children, the number of ways isΒ $$^{n+r-1}C_{r-1}=^{5+3-1}C_{3-1}=^7C_2=21$$

For cookies, there are six cookies and we need to give at least 1 to each child, the number of ways isΒ $$^{n-1}C_{r-1}=^{6-1}C_{3-1}=^5C_2=10$$

So, the total number of ways isΒ $$21\times10=210$$

Hence, the answer is 210.

Get AI Help

Video Solution

video

Create a FREE account and get:

  • Download Maths Shortcuts PDF
  • Get 300+ previous papers with solutions PDF
  • 500+ Online Tests for Free

Join CAT 2026 course by 5-Time CAT 100%iler

Crack CAT 2026 & Other Exams with Cracku!

Ask AI

Ask our AI anything

AI can make mistakes. Please verify important information.