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  • How many 4- digit numbers are there with no digit repeated?

  Q.2.    How many 4-digit numbers are there with no digit repeated?

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The thousands place of 4-digit numbers has to be formed by using the digits 1 to 9(0 cannot be included).

Therefore, the number of ways in which thousands  place can be filled is 9.

Hundreds,tens, unit place can be filled by any digits from 0 to 9.

The digit cannot be repeated in 4-digit numbers and thousand places is occupied with a digit.

Hundreds, tens, unit place can be filled by remaining any 9 digits.

Therefore, there will be as many 3-digit numbers as there are permutations of 9 different digits taken 3 at a time.

Therefore, the required number of 3-digit numbers =^{9}P_3

                                                                           =\frac{9!}{(9-3)!}

                                                                            =\frac{9!}{6!}

                                                                           =\frac{9\times 8\times 7\times 6!}{6!}

                                                                         =9\times 8\times 7=504

Thus, by multiplication principle, required 4 -digit numbers is  9\times 504=4536

 

 

 

Posted by

seema garhwal

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