You are making a number working with the digits 11235558 A H

You are making a number working with the digits 1,1,2,3,5,5,5,8. A) How many distinct ODD 8 digits numbers can you make using these digits? B) How many distinct 4 digit numbers can you make that are in strictly ascending order

Solution

A)

Since there is repetation in 1 and 5 with 2 times and three times respectively

therefore total no. distinct ODD 8 digits numbers can be made by using this

= 8! /(2!3!) =( 8x7x6x5x4)/2!

= 8x7x6x5x2

= 3360

(B) Since there is again repeatation

4 digit distinct number that can be written in strictly ascending order

can be written as

= ⁸C_{4 /2!*3! = 8! / (4!4!*2!*3!) = 5.83 = 6}

Hence answer is 6