A group of 10 people need to form a line. The line will consist of exactly 8 of the people. Person X and Person Y have to be either fifth or sixth in line. How many different orders are possible?

Question

Adrien Ritter

Mathematics

17 May, 09:22

A group of 10 people need to form a line. The line will consist of exactly 8 of the people. Person X and Person Y have to be either fifth or sixth in line. How many different orders are possible?

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Randy Beasley · Answer 1

Answer: N = 40,320

Step-by-step explanation:

To arrange 10 people to a line of 8 people.

The number of ways is n = 10P8.

But since the condition given states that 2 people must stay in two particular slots.

The number of possible arrangements becomes;

N = number of ways of arranging the remaining people * number of ways of arranging the other 2.

N = 8P6 * 2P2

N = 8!/2! * 2!

N = 20,160 * 2

N = 40,320 ways