SOLUTION: how many 3-digit numbers can be formed with 0,1,2,3,4,5,6,7 greater than 400?(repetition not allowed)

how many 3-digit numbers can be formed with 0,1,2,3,4,5,6,7 greater than 400?(repetition not allowed) 


Since the number has to be greater than 400, the first digit has to be only 4,5,6 or 7 (4 ways of choosing the 1st digit)

To choose the remaining 2 digits, we need to choose 2 from a set of 7 digits 
(since the first digit is already chosen and there are no repetitions allowed)

This can b done in C(7,2) ways = 7*6/2 = 21 ways

In the set of 2 digits, each set can be arranged in 2 ways.

Hence, the total number of combinations = 
Number of ways of choosing the 1st digit *
Number of ways of choosing 2 digits from the remaining 7 *
Number of ways of arranging the 2 digits

= 4 * 21 * 2 = 168.

So there are 168 three-digit numbers that can be formed.

:)