Homework Help

Find how many four digit numbers can be formed by seven digits 1,2,4,5,6,8 and 9 if any...

user profile pic

roshan-rox | Valedictorian

Posted July 10, 2013 at 8:10 PM via web

dislike 1 like

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.

1 Answer | Add Yours

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 10, 2013 at 8:56 PM (Answer #1)

dislike 1 like

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.

 

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes