How many 3-digit numbers can be formed by using the digits 1 to 9 if no digits is repeated?

Asked by Pragya Singh | 1 year ago |  89

##### Solution :-

Here, what matters is the order of digits. Thus, there are permutations of 9 different digits taken 3 at a time.

Therefore, the number of 3-digit numbers =

$$^9P_3=\dfrac{9!}{(9-3)!}=\dfrac{9!}{6!}$$

$$\dfrac{9\times 8\times 7\times 6!}{6!}$$

= 9×8×7=504

Answered by Abhisek | 1 year ago

### Related Questions

#### How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

#### Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

#### How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’,

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

(i) 4 letters are used at a time

(ii) all letters are used at a time

(iii) all letters are used but first letter is a vowel ?