Question

How many different ways can four team members from the group of fifteen be lined up for a photograph?

Answer 1

They are (15!)/(15-4)! ways.
=(15!)/(11!)
=15×14×13×12
=180×182
=32760 ways

Answer 2

To form a team of 4 from the 15 people:

Number of choices for the first person = 15 (That is, any of the 15 people)

Number of choices for the second person = 14 (That is, any of the 14, excluding the one chosen earlier)

Number of choices for the third person = 13 (That is, any of the 13, excluding the ones chosen earlier)

Number of choices for the fourth person = 12 (That is, any of the 12, excluding the ones chosen earlier)

Find the number of possible combinations:

Number of possible combinations = 15 x 14 x 13 x 12 = 32760

Answer: 32760 different combinations