Maths question about selections?

A florist has to make a floral arrangement. She has 6 banksias, 5 wattles and 4 waratahs. All the flowers of each kind are different. In how many ways can the florist make a bunch of 10 flowers if she has to use at least 3 of each kind?

Maths question about selections?
Choosing from the 1st to the 10th flowers, where the first 3 from banksias, next 3 from wattles, and next 3 from waratahs.



Number of ways is 6C3 * 5C3 * 4C3 * (6+5+4-3*3)C1

= 20 * 10 * 4 * 6C1

= 4800
Reply:Total number of flowers = 6 + 5 + 4 = 15

Number of flowers already chosen = 3 of each of the 3 types

= 3x3 = 9

Remaining 15-9 = 6 flowers to choose 1 as the 10th flower. Report It
Reply:3.



She needs to use 3 of each of 3 flowers. That takes care of 9 flowers. If she is making a bath of 10, that just leaves 1 other flower. So her choices are:



3 banksias, 3 wattles and 4 waratahs

3 banksias, 4 wattles and 3 waratahs

4 banksias, 3 wattles and 3 waratahs
Reply:Only 3. Since using 3 of each kind of flower starts you off with 9 flowers, and you have 3 to choose from, there are 3 different bunches of 10 flowers:

A. 4 banksias, 3 wattles, and 3 waratahs

B. 3 banksias, 4 wattles, and 3 waratahs

C. 3 banksias, 3 wattles, and 4 waratahs.



Hope this helps!