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## Homework Statement

A teacher would like to distribute 20 candies to 5 children, each of which receives at least two candies.

(a) Find the probability that at least one child receives at least 6 candies.

(b) Find the probability that at least one child receives at least 7 candies if at least one child receives at least 6 candies

## Homework Equations

Answer:

(a) P(requried) = ##1 - \frac {1} {C^{20-1}_{5-1}}##

= ##\frac {3875}{3876}##

(b) P(required) = ##\frac{\frac {3875}{3876}-\frac{5 C_{4-1}^{14-1}}{C_{5-1}^{20-1}}+\frac{C_2^5 C_{3-1}^{8-1}}{C_{5-1}^{20-1}}-\frac{C_3^5}{C_{5-1}^{20-1}}}{\frac {3875}{3876}}##

= ##\frac{529}{775}##

## The Attempt at a Solution

I thought of simplifying the problem at first.Because each child has to get at least 2 candies, so I thought of changing the question so that it becomes distributing 10 candies to 5 children with no restriction.

And then I have no idea what to do.

I looked at the answer but I couldn't work out what it is doing.

Please could someone give me some hints? Thanks.