Question

Evaluate 11c3 and 11p4

Answer 1

Answer:

11c3 = 165

11p4 = 7920

Step-by-step explanation:

To evaluate : 11c3 and 11p4

Solution:

Permutation refers to arrangement of objects such that order matters.

Combination refers to selection of objects such order does not matter.

$nCr=\frac{n!}{r!(n-r)!}\\nPr=\frac{n!}{(n-r)!}$

For n = 11 and r =3:

$11C3=\frac{11!}{3!(11-3)!}\\=\frac{11!}{3!8!}\\=\frac{11\times 10\times 9\times 8!}{3\times 2\times 8!}\\=\frac{11\times 10\times 9}{3\times 2}\\=165$

For n = 11 and r = 4:

$11p4=\frac{11!}{(11-4)!}\\=\frac{11!}{7!}\\=\frac{11\times 10\times 9\times 8\times 7!}{7!}\\=11\times 10\times 9\times 8\\=7920$

Answer 2

$_{n}C_{r} = \frac{n!}{r!(n-r)!} \\ \\ _{11}C_{3}= \frac{11!}{3!*(11-3)!} =\frac{11*10*9*8*7*6*5*4*3*2*1}{3*2*1*8*7*6*5*4*3*2*1} =\frac{11*10*9}{3*2} =165 \\ \\_{11}C_{4}=\frac{11!}{4!(11-4)!} =\frac{11*10*9*8*7!}{4!*7!} =\frac{11*10*9*8}{4*3*2*1} =330$