First slide

Combinations

Question

The number of ways in which thirty five apples can be distributed among 3 boys so that each can have any number of apples, is

Moderate

A

1332
B

666
C

333
D

None of these

Solution

Number of ways $=^{37} C_{2} = \frac{37!}{35! \times 2!} = 666 ways$
For the distribution equation.
$x_{1} + x_{2} + x_{3} + \dots + x_{r} = n$
The number of ways in which n things can be distributed among r in such a way each can receive none, one or more or all of n items are $^{n + r - 1} C_{r - 1}$

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