Thread: possible colour choices

I have a packet of M&M’s. M&M’s come in six possible colours: red, green,
blue, orange, yellow and brown. How many M&M’s need to be in the packet so that I

can be sure I have:

(a) At least five M&M’s of one colour.
(b) At least nine M&M’s of one colour.
(c) At least five red M&M’s.

Here are the answers (which I believe are correct)

(a)
(b)
(c) Impossible. There could be far too many non-reds.

Could someone explain to me how they worked out those answers for part (a) and part (b)? Why did they times those numbers?

Originally Posted by demode

I have a packet of M&M’s. M&M’s come in six possible colours: red, green,
blue, orange, yellow and brown. How many M&M’s need to be in the packet so that I

can be sure I have:

(a) At least five M&M’s of one colour.
(b) At least nine M&M’s of one colour.
(c) At least five red M&M’s.

Here are the answers (which I believe are correct)

(a)
(b)
(c) Impossible. There could be far too many non-reds.

Could someone explain to me how they worked out those answers for part (a) and part (b)? Why did they times those numbers?

6*4 refers to having 4 red, 4 green, ... , 4 brown M&Ms. This is the maximum number of M&Ms you can have and NOT necessarily have 5 of one colour. So, add 1 to it and you get your answer. Part (b) is exactly the same.