Question

Suppose we want to choose 7 colors, without replacement, from 11 distinct colors.

Answer 1

Answer:

(A) 1,663,200

(B)330

Step-by-step explanation:

(A) To do this you would just have to know the combimations formula which is $\frac{n!}{(n-r)!}$ and when you plug in the numbers you get $\frac{11!}{4!}$ which when simplified is $\frac{39,916,800}{24}$ which is 1,663,200

(B) To do this you would just have to know the permutation formula which is $\frac{n!}{r!(n-r)!}$ so if we plug in all of the numbers we would get $\frac{11!}{7!(4!)}$ then we can divide 7 from both sides so we get $\frac{(11)(10)(9)(8)}{(4)(3)(2)(1)}$ and when you simplify you get $\frac{7920}{24}$ which when reduced is 330