Question

In how many ways can 12 apples be distributed among john, grace and gloria, such that john gets at least 4, grace gets at least 2 and gloria gets at least 2?

Answer 1

Each one will get four cause there r 3 children and 12 apples.
$12 \div 3 = 4$

Answer 2

ANSWER:

We can distribute the 12 apples in 24 ways such that john gets at least 4, grace gets at least 2 and gloria gets at least 2

SOLUTION:

Given, 12 apples are to be distributed among john, grace and Gloria.

Such that, john gets at least 4, grace gets at least 2 and gloria gets at least 2.

We have to find how many ways are possible to distribute.

As we know john gets at least 4, grace gets at least 2 and gloria gets at least 2.

First let us give away the minimum number of apples to each person.

Now, john has 4 apples, grace has 2 apples, Gloria has 2 apples.

Then, remaining apples are 12 – 4 – 2 – 2 = 12 – 8 = 4 apples.

Now, 4 apples are to be distributed among 3 people.

$\begin{array}{l}{\text { Then number of different ways }=4 \mathrm{p} 3} \\ {=\frac{4 !}{(4-3) !}=\frac{4 !}{1 !}=4 !=24 \text { ways }}\end{array}$

Hence, we can distribute the apples in 24 ways.