Question

Let S={a, b, c, d, e}. Find the number of ways to select 7 elements from S when repetition is allowed. The order in which the elements are chosen does not matter

Answer 1

Since the number of elements S is less than the number of elements that

you need to choose and the order of selection does not matter, we will get the answer

using a formula to calculate combinations of 5 to 7 elements, namely:

$\bar{C}_5^7 = C_{11}^7 =C_{11}^{11-7} = C_{11}^4 = \dfrac{11!}{7!*4!} =\\ = \dfrac{11*10*9*8}{4*3*2*1} = 330\\ \space\\ answer: \space 330$