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A certain telephone number has 7 digits. If the telephone [#permalink]
01 Oct 2003, 16:47

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A certain telephone number has 7 digits. If the telephone number
has the digit 0 exactly three times, and the number one is not used at all,
what is the probability that the phone number contains 1 or more prime
digits?

the total number of combinations: _ _ _ _ _ _ _
3 zeroes=7C3, but this includes a zero on the first place. Eliminate this fact: 7C3–6C3. Four other positions can be filled with 8 digits each. In total, we have 8*8*8*8*[7C3–6C3]

the number of combinaions having no primes 4*4*4*4*[7C3–6C3]

The first digit cannot be zero and since 1 is not used the first digit can range from 2-9 = 8 combinations
In the remaining 6 places we have 3 zeros in 3! * 4! ways. The other three places can take any values from 2 to 9 ( 8 values per position)
Total combinations are 8 * 3! * 4! * 8^3 = 3!*4!*8^4
Desired combinations are atleast one prime = 1-P(no prime)
The only non primes are 2,4,6,8
Using the same technique com binations with no primes = 4*3!*4!*4^3
= 3!*4!*4^4

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