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Samples of Basic Algebra

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1. If a bag contains 15 marbles, how many samples of 2 marbles can be drawn from it? How many samples of 4 marbles can be drawn?

2. Seven workers decide to send a delegation of 2 to their supervisor to discuss their grievances.

a. How many different delegations are possible?

b. If it is decided that a certain employee must be in the delegation, how many different delegations are possible?

c. If there are 2 women and 5 men in the group, how many delegations would include at least 1 woman?

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Solution Preview

1. Marbles are each assumed to be different or distinct

Define r = 2 as the number of marbles that are drawn from n = 15 marbles in total

Number of samples s = n!/{r!(n - r)!} = 15!/{2!.(15 - 2)!} = 15!/2!.13! = (15 x 14)/(2 x 1) = 105 samples

If now r = 4, n = 15

s ...

Solution Summary

The solution answers different samples of basic algebra.