Question

There are 11 runners in a race. Medals are awarded for 1st, 2nd, and 3rd place. In how many different ways can the medals be awarded?

a.330

b.990

c.110

d.165

Answer 1

Then the number of the ways that the medals can be awarded will be 165. Then the correct option is D.

What are permutation and combination?

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

There are 11 runners in a race. Medals are awarded for 1st, 2nd, and 3rd place.

Then the number of the ways that the medals can be awarded.

$\rightarrow ^{11}C_3\\\\\\\rightarrow \dfrac{11!}{(11-3)! 3!}\\\\\\\rightarrow \dfrac{11 \times 10 \times 9 \times 8!}{8! \times 3 \times 2 }\\\\\\\rightarrow \dfrac{11 \times 10 \times 9}{3 \times 2}\\\\\\\rightarrow 11 \times 5 \times 3\\\\\\\rightarrow 165$

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255

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