A newly married couple plans to have 5 children. What is the probability that they will have 3 boys and 2 girls?

The number of ways of having 3 boys (B) and 2 girls (G) is the number of distinct arrangements of BBBGG. Therefore, the number of outcomes in the event is

number of ways to have 3 boys and 2 girls .

Each of the 5 children can be a boy or a girl. Using the Fundamental Counting Principle, the number of outcomes in the sample space is 2 ?- 2 ?- 2 ?- 2 ?- 2 = 32.

Therefore, the probability of having 3 boys and 2 girls is

The probability that they will have 3 boys and 2 girls is 0.3125 or 31.25%.

Some examples can be solved using combinations. Examples 3 and 4 explore this.

 A jar contains 35 nickels and 50 dimes. If 4 coins are chosen at random, what is the probability that the 4 coins total 25 cents?

If the 4 coins total 25 cents, they must be 3 nickels and 1 dime.

Because the order in which the coins are selected does not matter, use combinations.

The number of ways 3 nickels can be selected from 35 nickels is 35 C 3 .

The number of ways 1 dime can be selected from 50 dimes is 50 C 1 .

Using the Fundamental Counting Principle, the number of ways 3 nickels and 1 dime can be selected from the 85 coins in the jar is 35 C 3 ?- 50 C 1 .

The number of outcomes in the sample space is the number of ways 4 coins can be selected from the 85 in the jar, 85 C 4 .

The probability that the 4 coins total 25 cents is about 0.162 or 16.2%.