27. Coca Cola Directors There are 11 members on the board of directors for the C

Question

27. Coca Cola Directors There are 11 members on the board of directors for the Coca Cola Company. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?

34. Mega Millions As of this writing, the Mega Millions lottery is run in 12 states. Winning the jackpot requires that you select the correct five numbers between 1 and 56 and, in a separate drawing, you must also select the correct single number between 1 and 46. Find the probability of winning the jackpot.

Explanation / Answer

(a)

The chairperson can be elected in 11 ways, first vice chairperson in 10 ways, second vice chairperson im 9 ways and secretary in 8 ways. So possible number of committees are:;

10 9* 8 * 7 = 5040

(b)

Number of possible subcommittee of four members is:

C(11,4) = 11! / (4 *7!) = 330

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34:

Number of ways of seelcting 5 numbers out of 56 is C(56, 5) = 3819816

Number of ways of seelcting 1 number out of 46 is C(46, 1) = 46

So possible number of combinations are: 46 * 3819816 = 175711536

The probability of winning the jackpot is

P(jackpot) = 1 / 175711536 = 0.000000005691

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