Suppose that Professor Rodgers needs one small group of students from his class to participate in a focus group. There are 11 students in the class. How many different combinations of three selected students can Professor Rodgers create? number of combinations of three students: If Professor Rodgers decides he needs four students in the focus group, how many combinations can he create? number of combinations of four students:

(A) 165

(B) 330

Step-by-step explanation:

Total number of students in the class = 11

(A) How many different combinations of 3 selected students can he create?

ⁿCₓ = n! ÷ [(n - x)! x!]

n = 11,  x = 3

11! / [8! 3!]  = 165

HINT:  8! or 8 factorial represents [8x7x6x5x4x3x2x1]

(B) How many different combinations of 4 selected students can he create?

ⁿCₓ = n! ÷ [(n - x)! x!]

n = 11,  x = 4

11! / [7! 4!]  = 330

Same hint applies here, for all numbers with the factorial sign.

you can't solve x because it is 2 linear equation and you only have one equation