# Twelve Students Complete in a Race. in How Many Ways First Three Prizes Be Given? - Mathematics

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

#### Solution

Number of competitors in the race = 12
Number of  competitors who can come first in the race = 12
Number of  competitors who can come second in the race = 11    (as one competitor has already come first in the race)
Number of  competitors who can come third in the race = 10
∴ Total number of ways of awarding the first three prizes = 12$\times$11$\times$10 = 1320

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 13 | Page 15