Question

how many ways can you make 4 digit odd number from 0 1 2 3 4 5 without repeated numbers

Answer 1

Digits {0.,1,2,3,4,5}

Lets find out total 4-digit numbers

For the 1st place=5 ways {1,2,3,4,5}

For the 2nd place= 5 ways

For the 3rd place =4 ways

For the 4th place= 3 ways

Total numbers =5*5*4*3 = 300 (Even + Odd)

Now;

• Numbers starts with 1 = (300/5=60)
  Remaining digits {0,2,3,4,5} out of which 3 even digits and 2 odd.
  so even numbers =36 and odd numbers =24
• Numbers starts with 2 =60
  Even numbers =24
  Odd numbers =36.
  Similarly we get,

So Total Even numbers= 156

and Total Odd numbers= 144. Ans.