Question

Twelve students compete in a race. In how many ways first three
prizes be given?

Answer 1

=12!÷(12-3)!

=12!÷9!

=10x11x12

=1320

Answer 2

Answer:

$Number \:ways \: first \:3 \: prizes \\be\:given=1320$

Step-by-step explanation:

$Number \: students \: compete \: in \:a \:race=12$

$Number \:ways \: first \:3 \: prizes \:be\:given \\=3! \times ^{12}C_{3}$

$= 3! \times \frac{12!}{(12-3)! \times 3!}$

$= \frac{12!}{9!}\\=\frac{12\times 11\times 10\times9!}{9!}\\=12\times 11\times 10\\=1320$

Therefore,

$Number \:ways \: first \:3 \: prizes \\be\:given=1320$

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