To win at LOTTO in the state of Florida one must correctly s

To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible? To win in the New York State lottery, one must correctly select 6 numbers from 59 numbers. The order in which the selection in made does not matter. How many different selections are possible? In how many ways can a committee of four men and five women be formed from a group of seven men and seven women? How many different committees can be formed from 5 professors and 15 students if each committee is made up of 2 professors and 10 students? The US Senate of the 109th Congress consisted of 55 Republicans 44 Democrats, and 1 Independent. How many committees can be formed if each committee must

Solution

37 ) Total : 7 men and 7 women

Selection : 4 men and five women

So ways of selecting women 7C5

ways of selecting men 7C4

Total no. of ways of forming committees = 7C5*7C4 = 21*35 = 735