Question

Giselle is making flower arrangements for a party with 11 roses, 12 orchids, and 7 tulips. She wants three roses, eight orchids, and four tulips in each arrangement. How many different arrangements can Giselle make?

a) 462
b) 396
c) 572
d) 308

Answer 1

The different arrangements Giselle can make is 695 arrangements

How application of combination

To find the number of different arrangements Giselle can make, let's use the combination formula:

C(n, r) = n!/r!(n-r)!

where n! represents the factorial of n

For roses: C(11, 3) - Giselle chooses 3 roses out of 11.

For orchids: C(12, 8) - Giselle chooses 8 orchids out of 12.

For tulips: C(7, 4) - Giselle chooses 4 tulips out of 7.

Combine to find the total number of arrangements:

C(11, 3) +C(12, 8) + C(7, 4)

= 11!/3!(11-3)! + 12!/8!(12-8)! + 7!/4!(7-4)!

= 11!/3!8! + 12!/8!4! + 7!/4!3!

= (11*10*9/3*2) + (12*11*10*9/4*3*2*1) + (7*6*5/3*2*1)

=11*5*3 + 11*3*3*5 + 7*5

= 165 + 495 + 35

= 695 arrangements.

The different arrangements Giselle can make is 695 arrangement