Given:

The number of roots from Goa to Bombay is air and sea.

So, the number of ways to go from Goa to Bombay is ^{2}C_{1}

Given: The number of roots from Bombay to Delhi are: air, rail, and road.

So, the number of ways to go from Bombay to Delhi is ^{3}C_{1}

Hence, the number of ways to go from Goa to Delhi via Bombay is ^{2}C_{1} × ^{3}C_{1 }= 2 × 3 = 6 ways.

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?