Question

Jeanine Baker makes floral arrangements. She has 18 different cut flowers and plans to use 7 of them. How many different selections of the 7 flowers are​ possible?

Answer 1

Answer:

31,824 different selections

Explanation:

Since we are making selection, we will use the combination formula to find the  number of selections possible.

For example, If r objects are selected from a pool of n objects, this can be done in nCr different ways.

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

if Jeanine Baker makes floral arrangements with 18 different cut flowers and plans to use 7 of them, her selection can be made in 18C7 different ways.

$18C7 = \frac{18!}{(18-7)!7!}\\18C7 = \frac{18!}{11!7!}\\ 18C7 = \frac{18*17*16*15*14*13*12*11!!}{11!*7*6*5*4*3*2!}\\\\18C7 = \frac{18*17*16*15*14*13*12}{7*6*5*4*3*2!}\\18C 7 = \frac{3*17*16* 3*2*13}{2} \\18C7 = 31,824\ different\ selections$