# 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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Expert Answers

jeew-m | Certified Educator

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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