Find how many four digit numbers can be formed by seven digits 1,2,4,5,6,8 and 9 if any digit is selected without repetetion but with two odd digits and two even digits.



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Posted on (Answer #1)

Number of ways to select 1st digit = 7

Number of ways to select 2nd digit = 6

Number of ways to select 3rd digit = 5

Number of ways to select 4th digit = 4


So with out repetition number of 4-digit numbers that can be formed are `7xx6xx5xx4 = 840` .


We have 3 odd number and 4 even number in the set.

Ways to select two odds `= ^3C_2 = 3`

Ways to select two even `= ^4C_2 = 6`


Number of 4-digit numbers with two even and two odd `3xx6 = 18`

But we can rearrange these four digits within the number.


So total number of ways `= 18xx4! = 432`


So we can form 432 four digit numbers for the given condition.



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