Question

(6) How many different 4 digit numbers can be
formed, using the digits 2, 4, 5, 6, 7, 8, if
(a) repetition of digits is not allowed ?
(b) repetition of digits is allowed?

Answer 1

❏ Permutation

Question →

How many 4 digit numbers can be formed, using

2 , 4 , 5 , 6 , 7 , 8

1. Repetition is not allowed →

Clearly, the total number of 4- digit numbers is equal to the way of filing 4 places .

→ Total digits we have = 6

→ 1st place can be filled with 6 digits

→ 2nd place by 5 digits

→ 3rd place by 4 digits

→ 4th place by 3 digits .

→ Do total number of 4 digit number using given numbers = 6×5×4×3

→ 360 different 4 digits numbers can be formed .

2. When repetition is allowed →

If repetition is allowed then every place can be filled with 6 digits . So number of digits will be

→ 6×6×6×6

→ 1296 numbers

Answer 2

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(a)

Given ,

" Repetition of digits is not allowed "

The first palce can be filled in 6 ways by anyone of the 2, 4, 5, 6, 7, 8 digits

The second place can be filled in 5 ways by anyone of the remaining digits

The third place can be filled in 4 ways by anyone of the remaining digits

The fourth palce can be filled in 3 ways by anyone of the remaining digits

By multiplication principle ,

The required number of permutations = 6 × 5 × 4 × 3 i.e 360 ways

Hence , 360 is the required number of four digit number by using 2, 4, 5, 6, 7, 8 digits , when repetition of digits is not allowed

(b)

Given ,

" Repetition of digits is allowed "

The first , second , third and fourth palce can be filled in 6 ways by anyone of the 2, 4, 5, 6, 7, 8 digits

By multiplication principle ,

The required number of permutations = 6 × 6 × 6 × 6 i.e 1296 ways

Hence , 1296 is the required number of four digit number by using 2, 4, 5, 6, 7, 8 digits , when repetition of digits is allowed