Question

Eight athletes are entered in the 220 meter
sprint.
In how many different orders can the eight
sprinters finish?

Answer 1

Answer:

8!=40320

Step-by-step explanation:

SInce their are 8 athletes and 8 positions we can assume this: The first sprinter has 8 positions to end in, the next has 7 places to finish in, the third has 6 places and so on... Using this we can multiply these possibilities to find that the possibilities are 8×7×6×5×4×3×2 which results in 40320 (this function is known as a factorial and denoted !).

Answer 2

Different orders can the eight sprinters finish = 8! = 40320

How to find in how many different orders can the eight sprinters finish ?

• At the finish of sprint there will be 8 spots for 8 athletes.

• Firstly, for an athlete, there are 8 options. He can take any of those 8 options, after which there will be 7 options left for 7 athletes.

• Again, out of those 7 athletes, any one can take a spot after which there be 6 spots left for 6 athletes.

In this way, fo the last athlete , there will be only one spot left.

∴ Different orders so that eight sprinters can finish is

                    8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

• 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 is also called 8 factorial denoted by 8!

So, different orders can the eight sprinters finish = 8! = 40320

Find out more information about the permutation and combination here: https://brainly.com/question/11732255

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