Jessica runs a small landscaping business. (Please provide explanation)

Question

1.Jessica runs a small landscaping business. She has on hand 12 rose bushes, 16 small

shrubs, 11 types of evergreen seedlings, and 18 kinds of lilies. In how many ways can

Jessica fill an order if a customer wants:

Please help I don't understand, explain if you can!

a) 15 varieties consisting of 4 roses, 3 shrubs, 2 evergreens, and 6 lilies?

b) Either 4 different roses or 6 different lilies?

Answer 1

Hi Mel,

This is a classic statistic question that employs permutations:

a) Out of 12 rose bushes, Jessica wants 4 -> Therefore we have 12 choose 4, which is 12!/(4!8!) = 495

Out of 16 small shrubs, Jessica wants 3 -> Therefore we have 16 choose 3, which is 16!/(13!3!) = 560

Out of 11 evergreens, Jessica wants 2 -> Therefore we have 11 choose 2, which is 11!/(9!2!) = 55

Out of 18 lilies, Jessica wants 6 -> Therefore we have 18 choose 6, which is 18!/(12!6!) = 18,564

Add these together and you will have the total ways to fufill this order.

b)Add 495 + 18564 = 19059