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Probability / Statistics : Combination Application Word Problems

In a marketing survey, consumers are asked to give their first three choices, of 9 different drinks. In how many different ways can they indicate their choices?

Find the present value of an ordinary annuity with annual payments of $1,000, for 6 years, at 10% interest compounded annually.

A class consists of 15 students. The instructor wants to pick a group of 4 to work on a special project.
a. How many different groups of 4 can he choose?
b. If the class consists of 10 girls and 5 boys, how many different groups of 4 are made up of 2 boys and 2 girls?

How many license plates can a state have if each license plate has 2 letters followed by 4 digits, if the first digit cannot be zero?

Two cards are drawn at random from an ordinary deck of playing cards. The first is not replaced before the second is drawn. What is the probability that:
a. Both cards are aces?
b. At least one card is black?

Solution Preview

1. In a marketing survey, consumers are asked to give their first three choices, of 9 different drinks. In how many different ways can they indicate their choices?
To select 3 out of 9, the total number of different ways is
C(9,3)=9!/(3!*6!)=84

2. Find the present value of an ordinary annuity with annual payments of $1,000, for 6 years, at 10% interest compounded annually.
Suppose the present value is x. After 1 year, the balance is x*(1+10%)-1000=1.1x-1000; after 2 years, the balance is 1.1(1.1x-1000)-1000=x*1.1^2-1.1*1000-1000. And so on.
Then after 6 years, ...

Solution Summary

This solution solves several world problems, addressing probability, compound interest and statistics.

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