Question

Evaluate the expression 11C4.

Answer 1

The correct answer is: 330

Explanation:

The formula for combination is given as follows:

$^nC_r = \frac{n!}{r! (n-r)!}$ --- (1)

Where n = 11

r = 4

Plug in the values in equation (1) and calculate:

$^nC_r = \frac{n!}{r! (n-r)!} \\ ^{11}C_{4} = \frac{11!}{4! (11-4)!} \\ ^{11}C_{4} = \frac{11*10*9*8*(7!)}{4! (7)!} \\ ^{11}C_{4} = \frac{11*10*9*8}{4!} \\ ^{11}C_{4} = \frac{11*10*9*8}{4*3*2*1} \\ ^{11}C_{4} = 330$

Hence the correct answer is 330.

Answer 2

11 C 4 = 11 ! / 4 ! ( 11-4 ) ! =  11! / 4! *7! = 11! / 4 ! =
= (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330