one is asked to say a 3 digit number .what is the probability that a)all the digit of the numbers are same?b)number is a multiple of 6?
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5
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6
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A three digit number starts from 100 and ends to 999. So, the numbers that are multiple of 6 are
102,108,114,120,126,…..996
As we know that, T(subscript)n=a+(n-1)d
996=102+(n-1)6
996=96+6n
6n=996–96
6n=900
n=900/6=150
n=150
So there are 150 numbers between 100 & 999 which are multiples of 6.
And the total numbers of three digit numbers=900
Probability of getting a 3 digit number between 100 & 999 which is multiple of 6=
150/900=15/90=5/30=1/6
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