Combinations with Repetitions Examples1

In this class, We discuss Combinations with Repetitions Examples1.

The reader should have prior knowledge of combinations with repetitions formulae. Click Here.

Example:

There are three boxes of identical red, blue, and white balls.

Several ways to select ten balls?

1) No restriction

This example exactly matches the formulae.

X = 10

N = 3

(X + N -1) C X

(3+ 10 -1) C 10

12 C 10.

2) Select at least one red ball, two blue, and three white balls.

R, B, B, W, W, W, are fixed.

The remaining selctions are X = 4

N = 3

(X + N -1) C X

(4 + 3 – 1) C 4

6 C 4

3) Exactly one red ball must be selected

One Red must be taken.

The remaining nine selections.

X = 9

Here, we are not going to select red again. So N = 2.

(X + N -1) C X

(9 + 2 -1) C 9

10 C 9

4) At most, one white ball.

We can take zero white balls or one white ball.

The reader can try this on their own.

Output: = 21