How many four-digit numbers will not exceed 7432 if they are formed us

1.	How many four-digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?
Answer» Between any set of digits, the greatest number is possible when digits are arranged in descending order. ∴ 7432 is the greatest number, formed from the digits 2, 3, 4, 7. Since a 4-digit number is to be formed from the digits 2, 3, 4, 7, where repetition of the digit is not allowed, 1000’s place digit can be selected in 4 ways, 100’s place digit can be selected in 3 ways, 10’s place digit can be selected in 2 ways, Unit’s place digit can be selected in 1 way. ∴ Total number of numbers not exceeding 7432 that can be formed with the digits 2, 3, 4, 7 = Total number of four-digit numbers possible from the digits 2, 3, 4, 7 = 4 × 3 × 2 × 1 = 24

How many four-digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?

Answer»

Between any set of digits, the greatest number is possible when digits are arranged in descending order.

∴ 7432 is the greatest number, formed from the digits 2, 3, 4, 7.

Since a 4-digit number is to be formed from the digits 2, 3, 4, 7, where repetition of the digit is not allowed,

1000’s place digit can be selected in 4 ways,

100’s place digit can be selected in 3 ways,

10’s place digit can be selected in 2 ways,

Unit’s place digit can be selected in 1 way.

∴ Total number of numbers not exceeding

7432 that can be formed with the digits 2, 3, 4, 7

= Total number of four-digit numbers possible from the digits 2, 3, 4, 7

= 4 × 3 × 2 × 1

= 24