Three out of seven students in the cafeteria line are chosen to answer survey questions. How many different combinations of three students are possible? 7 C 3 = StartFraction 7 factorial Over (7 minus 3) factorial 3 factorial 7 35 70 210

The number of different combinations of three students that are possible is 35.

Step-by-step explanation:

Given that three out of seven students in the cafeteria line are chosen to answer a survey question.

The number of different combinations of three students that are possible is given as:

7C3 (read as 7 Combination 3)

xCy (x Combination y) is defines as

x! / (x-y) ! y!

Where x! is read as x - factorial or factorial-x, and is defined as

x (x-1) (x-2) (x-3) ... 2*1.

Now,

7C3 = 7! / (7 - 3) !3!

= 7!/4!3!

= (7*6*5*4*3*2*1) / (4*3*2*1) (3*2*1)

= (7*6*5) / (3*2*1)

= 7*5

= 35

Therefore, the number of different combinations of three students that are possible is 35.

35

Step-by-step explanation:

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