(a) You flip a coin ten times. Each flip comes up either heads or tails. How man
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Question
(a) You flip a coin ten times. Each flip comes up either heads or tails. How many possible outcomes will contain the same number of heads and tails? [Note: order matters. The outcome TTTTTHHHHH is different from the outcome THTHTHTHTH, but both contain equal number of heads and tails] (b) The Music department of the University of lowa has seven women and nine men on the faculty. In how many ways a committee of five members of the department can be selected if at least one woman must be on the committee?Explanation / Answer
Total no. of way in which there is at least 1 women= Total committees- total committees with no women
Now, total no. of committees are simply, that we have to select 5 people of 16(7 women and 9 men), so 16C5.
Now, total no. of committees with no women is simply, that we have to select 5 people of 9 men only, so 9C5.
So, answer is 16C5- 9C5= 4368- 126= 4242
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