Question

Compute the number of different ways to select a group of 4 out of 7 people for a seating arrangement in a row of length 4 when n = 7 and k = 4.

Answer 1

The number of different ways to select a group of 4 out of 7 people for a seating arrangement in a row of length 4 is 35.

Step-by-step explanation:

The number of different ways to select a group of 4 out of 7 people for a seating arrangement in a row of length 4 can be calculated using combinations.

The formula for combinations is nCr, where n represents the total number of objects and r represents the number of objects to be selected.

In this case, n = 7 and r = 4. So the number of ways to select a group of 4 out of 7 people is given by:

nCr = 7C4 = 7! / (4!(7-4)!) = 7! / (4!3!) = (7*6*5) / (3*2*1) = 35

Therefore, there are 35 different ways to select a group of 4 out of 7 people for a seating arrangement in a row of length 4.