1(a) How many different orders are possible for completing the race?
8*7*6*5*4*3*2*1=8!=40,320
(b) In how many different ways can first, second, and third places be decided? (Assume there is no tie.)
(8*7*6)=P(8,3)=336 or 6*C(8,3) where 6=3*2*1 the number of ways of arranging three items
2.)Telephone numbers consist of seven digits; the first digit cannot be 0 or 1. How many telephone numbers are possible?
8*10^6=8,000,000
3.)In how many ways can five people be seated in a row of five seats?
5*4*3*2*1=5!=120
4.)In how many ways can five different mathematics books be placed next to each other on a shelf?
5!=120
5.)In a family of four children, how many different boy-girl birth-order combinations are possible? (The birth orders BBBG and BBGB are different.)
16=2*2*2*2 from BBBB to GGGG
6.)Two cards are chosen in order from a deck. In how many
ways can this be done if
(a) the first card must be a spade and the second must be a
heart?
13*13=169
(b) both cards must be spades?
13*12=156
7.)A company’s employee ID number system consists of one letter followed by three digits. How many different ID numbers are possible with this system?
26*10*10*10=26,000
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