Combinations and Permutations

Question

How many even numbers less than 500 can be formed using the digits 1,2,3,4,5. can be used once only

ans 28

 

2)(i) find how many different 4 digit numbers can be formed using the digits 1,2,3,4,5,6, if no digits are repeated (ans 360)

(ii) how many of the 4 digit number found in part (i) are greater than 6000? (ans 60)

(iii)how many 4 digits numbers found in part (i) are greater than 6000 and are odd?

Answer 1

In order for a number to be >6000 and odd, we know the first digit must be 6 and the last number must be 1, 3 or 5.

 

6 (any of the 4 remaining numbers besides the final odd) (any of the 3 remaining) (the 3 odds)

 

Which gives us 1 * 4 * 3 * 3 = 36 combinations.