Question

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

Answer 1

The number of four digit numbers will not

exceed 7432 if they are formed using the

digits 2,3,4,7 without repetition are 24.

Step-by-step explanation:

The total number of permutations using the digits 2, 3, 4, 7 without repetition is $4\times3\times2\times1=24$.

Since 7432 is the largest number that we can make using the digits 2, 3, 4 and 7 is 24.

Therefore, the total number of four digit numbers will not exceed 7432 using the digits 2, 3, 4, 7 without repetition is 24.

Or in another way, the number of permutations starting with the digit 2 is $1\times3\times2\times1=6$. Since the first place is filled by the digit 2, the second place can fill by the remaining 3 digits, the third place can be filled  by 2 digits,and the last place can be filled by only one digit because repetition is not allowed.

similarly, the total number of permutations starting with the digits 3 and 4 is 6+6=12.

Now the number of permutations starting with the digit 7 are as follows:

7432, 7423, 7342, 7324, 7243, 7234.

Of these numbers, no number is exceed 7432.

Therefore, The total number of four digit numbers will not exceed using the digits 2, 3, 4, 7 without repetition is 6+6+6+6=24.

Answer 2

The number of four digit numbers that will not exceed 7432 will be 24.

Step-by-step explanation:

We first have to calculate the number of four-digit numbers formed from the digits 2, 3, 4, 7 without repetition.

So, the digits 2, 3, 4, and 7 can be arranged taken four at a time without repetition in $^4P_4 = 24$ ways.

Now, the number 7432 is the largest number of all the possible four-digit numbers.

So, each and every number in the arrangement are less than 7432 and the number of four-digit numbers that will not exceed 7432 will be 24. (Answer)