The required numbers are greater than 7000.

So, the thousand’s place can be filled with any of the 3 digits: 7, 8, 9.

Let us assume four boxes, now in the first box can either be one of the three numbers 7, 8 or 9, so there are three possibilities which are ^{3}C_{1}

In the second box, the numbers can be any of the four digits left, so the possibility is ^{4}C_{1}

In the third box, the numbers can be any of the three digits left, so the possibility is ^{3}C_{1}

In the fourth box, the numbers can be any of the two digits left, so the possibility is ^{2}C_{1}

Hence, the total number of possible outcomes is ^{3}C_{1} × ^{4}C_{1} × ^{3}C_{1} × ^{2}C_{1} = 3 × 4 × 3 × 2 = 72.

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?