Odd Numbers Only

Probability Level 2

How many odd numbers greater than 40000 40000 can be formed from the digits 1 , 2 , 3 , 4 1,2,3,4 and 5 5 ? Repetition of digits is not allowed.

Marvin's Math Quiz 1

30 36 18 24

A Former Brilliant Member by A Former Brilliant Member

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1 solution

if 4 is the leading digit, there are 1(3)(2)(1)(3) = 18 numbers

if 5 is the leading digit, there are 1(3)(2)(1)(2) = 12 numbers

total = 18 + 12 = 30 numbers

2 Helpful 1 Interesting 0 Brilliant 0 Confused

If the leading digit 4 can't we form the number by 24 way???

shithil Islam - 4 years, 4 months ago

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No because we are considering odd numbers only, there are only three odd digits (1,3 and 5).So we can put any of the three odd digits on the unit's place. Since we put a digit on the ten thousands place (digit 4) and a digit on the unit's place (any of the three odd digits), we can arrange the three remaining digits by 3! ways. So, 1 x 3 x 3! = 18 ways

A Former Brilliant Member - 4 years, 4 months ago

oops sorry I didn't see the "odd number".... my mistake..

shithil Islam - 4 years, 4 months ago

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