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 P₁, P₂, P₃ …, P₁₀. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement P₁ must occur whereas P₄ and P₅ 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?