5) I have a group of a dozen students. Six are female. If I randomly select six

Question

5) I have a group of a dozen students. Six are female. If I randomly select six of the 12 students, what is he probability I get all all of the same gender? 16) The lottery you are going to play has you win if you can pick the 6 correct numbers out of 1-50 AND a powerball digit, 0-9. probability you win if you buy 50 tickets? b) What is the a) What is the probability you win with one ticket? 17) How many ways could I choose 10 people out of a room of 40 people if order m If order didn't matter? attered? 18) How many different phone numbers can we form if we cannot have a zero or area code and we cannot have a O or 1 in the front of the main 7 digit number? 1 in the beginning of the 19) How many ways could I order seven red chips and nine blue chips? can I do so? 20) I need to place seven books in a linear display in a bookstore window. How many ways

Explanation / Answer

15) total number of students = 12

6 are male and 6 are female.

Probability of selecting 6 males = 6C6 / 12C6

Probability of selecting 6 females = 6C6 / 12C6

Probability that all of them are of same gender =  (6C6 / 12C6 )+  (6C6 / 12C6) = 2/924 =  

17) I can choose 10 people out of 40 people ( if order does not matter) in 40C10 ways =

I can choose 10 people out of 40 people ( order matters) in 4! 40C10 =

19) total number of chips = 7+9 = 16

We can order them in 16! / (7!*9!) ways

= 11440 ways.

because 7 red chips are identical and 9 blue chips are also identical.

20) The number of ways i can place 7 books in a linear display is 7! = 5040 ways.

i.e. 7*6*5*4*3*2*1 ways

for first book there are 7 places (options).

for second book there are 6 options.

...................

...

for 6 th book there are 2 options.

finally for 7 th book only 1 option is left.

0.002165

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