one fashion book

[sanju09]

There are eight magazines, including 4 fashion books and 4 sports books. If three books are to be selected at random without replacement, what is the probability that at least one fashion book will be selected?
A. 1/2
B. 2/3
C. 32/35
D. 11/12
E. 13/14



OA E

[moutar]

P(at least one fashion book) = 1 - P(no fashion books)
= 1 - P(SSS)
= 1 - (4/8 * 3/7 * 2/6)
= 1 - 1/14
= 13/14


[1st choice: 4 out of 8 books are fashion
2nd choice: 3 out of 7 remaining books are fashion
3rd choice: 2 out of 6 remaining books are fashion]

[dendude]

Slightly different approach,
Prob that no fashion mag selected,
(4C3)/(8C3)
4C3 - for the combinations of 3 mags within the 4 sports mags
8C3 - for the combination of 3 mags within (4 + 4) mags
= 1/14

Prob that atleast one fashion mag selected, 1 - 1/14 = 13/14
Ans E