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course mth 164
1:30 pm Aug 4
13.27. P (6, 2)
P(n, r)= n!/(n-r)!
P(6, 2)= 6 * 5 (two factors)
= 30
8. P (7, 2)
= 7 * 6= 42
9. P ( 4, 4)
= 4 * 3* 2* 1 (four factors)= 24
10. P (8, 8)
= 8 * 7 * 6* 5 * 4 *3 * 2
= 40, 320
14. P (8, 3)
= 8 * 7 * 6
=336
15. C (8, 2)
C (n, r)= n!/ (n - r)! r!=
8!/ (8-2)! 2!= 8 *7*6*5/6*2
=8 *7*5/2!= 28
18. C (6, 2)
6!/ (6-2)! 2!= 6*5*4*3/ 4!2!
= 6* 5*3/2= 90/2= 45
20. C (18, 1)
= 18!/ (18 -1)! 1!=
27. a, b, c, d, e taken 3 at a time C (5, 3)
{abc, abd, abe, acd, ace, ade, bcd, bde, bce, cde}
C (5, 3)
C (n ,r)= n!/(n- r)! r!= C (5, 3)= 5!/(5-3)!3!
= 5*4*3*2/ 2!3!= 5*4/2= 10
30. 6 objects (1, 2, 3, 4, 5, and 6) and 6 are taken 3 at a time. What is C (6, 3)?
P (6, 3)
= 6*5*4= 120
C(6, 3)= C(n, r)= n!/(n- r)! r!=6!/ (6-3)!3!= 6*5*4*3/ 3!3!= 6*5*4/6!= 20
33. number of 3 digit numbers that can be formed using the digits 0 and 1= 8.
35. How many ways can 4 people be lined up? 24 ways
13.3
7. Outcome Probability
1 .2
2 .3
3 .1
4 .4
Because all the outcomes have probabilities that are nonnegative and the sum of the probabilities is one, this is a probability model.
10. Probabilities
.3
.2
.1
.5
-.1
This is not a probability model because it has a number less than 0 (negative.)
11. tossing a fair coin twice
S= HH, HT, TH, TT
P(TH)= ¼
P (HH)= ¼
P(HT)= ¼
P (TT)= ¼
14. Tossing a fair coin, a fair die, and then a fair coin
S= {HH1, HH2, HH3, HH4, HH5, HH6, TT1, TT2, TT3, TT4, TT5, TT6, HT1, HT2, HT3, HT4, HT5, HT6}
23. A, B, F, and C.
27. The probability for heads would be 4/5 and the probability of tails would be 1/5.
44. probability that the sum of the two dice is two..1/11
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