Permutation and Combination

What is the number of possible words that can be made using the word “EASYQUIZ” such that the vowels always come together?

What is the number of possible words that can be made using the word “QUIZ” such that the vowels never come together?

How many five-letter words can be made from the word “APPLE” using all the alphabets with repetition and without repetition, respectively?

How many ways a 6 member team can be formed having 3 men and 3 ladies from a group of 6 men and 7 ladies?

In how many ways can an interview panel of 3 members be formed from 3 engineers, 2 psychologists and 3 managers if at least 1 engineer must be included?

How many 4-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 which are divisible by 5 when none of the digits are repeated?

In how many ways can 20 boys and 18 girls make a queue such that no two girls are together?

There are 5 floating stones on a river. A man wants to cross the river. He can move either 1 or 2 steps at a time. Find the number of ways in which he can cross the river? (Man can't take double step from last stone).

Out of 7 boys and 4 girls, how many queues of 3 boys and 2 girls can be formed?

A box contains 2 red coins, 3 green coins and 4 blue coins. In how many ways can 3 coins be chosen such that at least one coin is green?