A dance instructor chose four of his 10 students to be on stage for a performance. If order does not matter, in how many different ways can the instructor choose the four students? sub 10 cap c sub 4 is equal to the fraction with numerator 10 factorial and denominator open paren 10 minus 4 close paren factorial 4 factorial
Because order does not matter, use combinations: choose(10, 4) = 10! / (6! × 4!). Canceling the 6! gives (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1) = 210. The correct choice is 210.
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