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open the safe please! (counting and probablity)

Expert replies
by ashish1354 » Sat Sep 19, 2009 12:31 am
. A seven-digit combination lock on a safe has zero exactly three times, does not have the digit 1 at all. What is the probability that exactly 3 of its digits are odd?

(a)1/2
(b)1/3
(c)1/6
(d)4/16
(e)9/16
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Source: — Problem Solving |

by praky_rules » Sat Sep 19, 2009 10:34 am
exactly three digits are zeros.
No 1 at all.

Remaining 4 numbers, out of which exactly 3 need to be odd.

Even Nos = 2,4,6,8
Odd Nos = 3,5,7,9

Prob. of odd no = 1/2

Probably of exactly 3 odd numbers = 4C3*(1/2)^3*(1/2)^2.

4/16.
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