Question

Suppose that a cookie shop has three different kinds of cookies. How many different ways can five cookies be chosen?

Answer #1

Number of cookies to be chosen, n = 5

And, total variety of cookies are 3. Suppose, there are 3 types of cookies, A, B & C.

Suppose, we choose x cookies of type A, y cookies of type B & z cookies of type C.

Then, we need to find all possible non-negative integral solutions of, x + y + z = 5

The number of non-negative integral solutions of the equation
is, ^{5+3-1}C_{3-1} =
^{7}C_{2} = 21

So, there are 21 different ways to choose five cookies from the lot.

A national youth organization sells six different kinds of
cookies during its annual cookie campaign. A local leader is
curious about whether national sales of the six kinds of cookies
are uniformly distributed. He randomly selects the amounts of each
kind of cookies sold by five youths and combines them into the
observed data that follow. Use = .05 to determine whether the data
indicate that sales for these six kinds of cookies are uniformly
distributed.
Kind of Cookie
ObservedFrequency...

A national youth organization sells six different kinds of
cookies during its annual cookie campaign. A local leader is
curious about whether national sales of the six kinds of cookies
are uniformly distributed. He randomly selects the amounts of each
kind of cookies sold by five youths and combines them into the
observed data that follow. Use α = .05 to determine whether the
data indicate that sales for these six kinds of cookies are
uniformly distributed.
Kind of Cookie...

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How many ways are there to distribute 15 cookies between5
children such that:
(a) zero or more cookies?
(b) at least 1 cookie?
-----------------
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Discrete math
A candy shop has 11 different color of gum ball.
1. How many ways are there to fill one bag, assume 6 gum ball
are 1 bag.
2. How many ways are there to fill one bag of 6 gum ball, if
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