Question

Q. 11] How many 4 digit numbers not exceeding 4321 can be formed with the digits 1,2,3,4, if repetition of the digits is not allowed?

Answer 1

Answer:

the total number of cases are: 23

Step-by-step explanation:

As the repetition of digits is no allowed

number starting from 1:

In this we have six cases as the first place is fixed for 1 and the repetition is not allowed so at second place there is only a possibility of 2,3,4. after second place only two possibilities left for third place and for the last place only 1 possibility will be left.

Hence number of cases that 1 will be in starting position=1×3×2×1=6

number starting from 2:

In this we have six cases as the first place is fixed for 2 and the repetition is not allowed so at second place there is only a possibility of 1,3,4. after second place only two possibilities left for third place and for the last place only 1 possibility will be left.

Hence number of cases that 2 will be in starting position=1×3×2×1=6

number starting from 3:

similar case holds.

Hence number of cases that 3 will be in starting position=1×3×2×1=6

number starting from 4:

as number could not exceed 4321 so the possible number left are: 4231,4312,4213,4123,4132

hence number starting from 4 there are 5 cases.

Hence, the total 4 digits number that can be formed using 1,2,3,4 such that the number do not exceed 4321 is :6+6+6+5=23.