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16 Mar 2004, 17:32
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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?
A) 1/24
B) 1/16
C) 1/2
4) 15/16
5) 23/24
Vivek.
A) 1/24
B) 1/16
C) 1/2
4) 15/16
5) 23/24
Vivek.
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16 Mar 2004, 17:44
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The number = abcdefgh
a != 0, exactly 3 zero-s appear in "bcdefgh"
a can be filled with 8 digits(all but 0 and 1)
3 zero-s 6C3
remaining 3 slots can be filled in 8^3
total #s = 6C3*8^4
total #s contain no prime digits(2, 3, 5, 7) = 6C3*4^4
Answer = 1 - (6C3*4^4/6C3*8^4) = 15/16
a != 0, exactly 3 zero-s appear in "bcdefgh"
a can be filled with 8 digits(all but 0 and 1)
3 zero-s 6C3
remaining 3 slots can be filled in 8^3
total #s = 6C3*8^4
total #s contain no prime digits(2, 3, 5, 7) = 6C3*4^4
Answer = 1 - (6C3*4^4/6C3*8^4) = 15/16
