Question

How many 4 digit numbers can be formed by using thr digits 1 to 9 if repetition of digits is not allowed from permutation nd combination chapter

Answer 1

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Answer 2

Answer:

Total 3024 , 4 digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed.

Step-by-step explanation:

• To Find 4−digit number using digits 1 to 9 when repetition is not allowed.

• Total number from 1 to 9  (n) = 9

• Required digits (r) = 4

∴ required 4−digit number= $9_{P_{4} }$

= $\frac{9!}{(9 - 4)!}$

=$\frac{9!}{5!}$

=$\frac{9*8*7*6*5!}{5!}$

=9×8×7×6

= 3024

• A permutation is used to determines the number of possible arrangements in a set when the order of the arrangements matters.

• The general  formula of permutation is expressed in the following way:

• Permutation - Formula : P(n,r) = n! / (n-r)!

     Where:

     n is the total number of elements in a given set

     r is the number of selected elements arranged in a specific order

     ! is factorial

• Factorial is the product of all positive integers which are less than or equal to the number preceding the factorial sign(!).