Question

In how many ways can 3 pears chosen at random from a bag of 60 pears?

Answer 1

$60C_3 \\ \\ = \frac{60 \times 59 \times 58}{6} \\ \\ = 59 \times 58 \times 10 \\ \\ = 34220 \: ways$

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Answer 2

Number of ways can be chosen = 34220

Given: number of pears in the bag = 60

Number of pear that can be chosen at a time = 3

To find: Number of way to chosen 3 pears at a time

Solution: The formula for combinations is given by

nC$_{r}$ = $\frac{n!}{r!(n-r)!}$  here n = number of total items = 60

and r = number of chosen items = 3

Therefore, number of way can be chosen = $\frac{60!}{3!(60-3)!}$  

= $\frac{60(59)(58)57!}{3!(57!)}$

= $\frac{60(59)(58)}{3(2)1}$

= $10(59)(58)$ = 34220  

The number of ways can be chosen = 34220.

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