In a nine-digit number, 0 cannot appear in the first digit and the repetition of digits is not allowed. So, the number of ways of filling up the first digit is ^{9}C_{1}= 9

Now, 9 digits are left including 0. So, the second digit can be filled with any of the remaining 9 digits in 9 ways.

Similarly, the third box can be filled with one of the eight available digits, so the possibility is ^{8}C_{1}

The fourth digit can be filled with one of the seven available digits, so the possibility is ^{7}C_{1}

The fifth digit can be filled with one of the six available digits, so the possibility is ^{6}C_{1}

The sixth digit can be filled with one of the six available digits, so the possibility is ^{5}C_{1}

The seventh digit can be filled with one of the six available digits, so the possibility is ^{4}C_{1}

The eighth digit can be filled with one of the six available digits, so the possibility is ^{3}C_{1}

The ninth digit can be filled with one of the six available digits, so the possibility is ^{2} C_{1}

Hence the number of total possible outcomes is ^{9}C_{1} × ^{9}C_{1} × ^{8}C_{1} × ^{7}C_{1} × ^{6}C_{1} = 9 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 = 9 (9!)

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.

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 ?

There are 10 persons named P_{1}, P_{2}, P_{3} …, P_{10}. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement P_{1} must occur whereas P_{4} and P_{5} do not occur. Find the number of such possible arrangements.

How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?