Probability: Mastering Permutations and Combinations (TONS OF EXAMPLES) by Code Duo

Author:Code, Duo [Code, Duo]
Language: eng
Format: epub
Published: 2017-07-24T16:00:00+00:00

To select the red number, you need:

C(35, 1) = 35 ways

Thus, the total number of tickets is:

C(59, 5) *P(35, 1) = 5006386*35 = 175223510 ways

Example 4.3: A bag contains 15 marbles. Out of these 15 marbles, 10 are red while 5 are white. Now, 4 marbles are chosen from the bag.

Before you begin to figure out how you’ll count, you should understand the ambiguity in this problem. Suppose on the first draw, you select four red marbles, and on the second draw, you choose different 4 marbles, are they considered the same sample or not?

In this problem, we’ll assume that they are not the same sample. For instance, you could imagine that the marbles are numbered with each having a different number so that you can distinguish marbles of the same color. This way of thinking will be very helpful for calculating probabilities later.

Let us now answer some questions regarding the bag containing 15 marbles.

a) How many are (different) samples of size 4 possible?

Solution

The order of counting doesn’t matter, but the numbers do so we are choosing the 4 elements from a set of (10 + 5) elements. Therefore, the number of different samples of size 4 are:

C (15, 4) = 1365

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