Math help Pls..

Question

1.Nine apples are randomly taken from a set of 4 red apples,5 green apples and 6 yellow apples.How many possibilities that 2 apples from all colours and minimum 4 yellow apples are taken?

A.20160
B.7560
C.5400
D.2160
E.800

Answer 1

In order to meet your minimum requirements, we could have 2 red apples, 2 green apples, and 5 yellow apples OR 2 red apples, 3 green apples, and 4 yellow apples OR 3 red apples, 2 green apples, and 4 yellow apples. Let's treat each case separately.

 

As a reminder, (5 choose 2) = ₅C₂ = 5!/(2!(5-2)!) = (5×4×3×2×1)/(2×1(3!)) = (5×4×3)/(3×2×1) = 20/2 = 10.

 

 

 

2 RED / 2 GREEN / 5 YELLOW:

 

(4 choose 2) = 6 ways to choose red apples

(5 choose 2) = 10 ways to choose green apples

(6 choose 5) = 6 ways to choose yellow apples

 

6×10×6 = 360 ways to choose two reds, two greens, five yellows

 

 

 

2 RED / 3 GREEN / 4 YELLOW:

 

(4 choose 2) = 6 ways to choose red apples

(5 choose 3) = 10 ways to choose green apples

(6 choose 4) = 15 ways to choose yellow apples

 

6×10×15 = 900 ways to choose two reds, three greens, four yellows

 

 

 

3 RED / 2 GREEN / 4 YELLOW:

 

(4 choose 3) = 4 ways to choose red apples

(5 choose 2) = 10 ways to choose green apples

(6 choose 4) = 15 ways to choose yellow apples

 

4×10×15 = 600 ways to choose three reds, two greens, four yellows

 

 

 

That's a total of 360 + 900 + 600 = 1860 ways to choose the apples.