What is the number of ways of choosing 4 cards from a deck of 52 cards? In how many of these,

(a) 3 are red and 1 is black.

(b) All 4 cards are from different suits.

(c) are face cards.

(d) All 4 cards are of the same suit.

Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of these arrangements,
i) do the words start with p

ii) do all the vowels always occur together

iii) do all the vowels never occur together

iv) do the words begin with I and end in P?

If all letters of word ‘MOTHER’ are written in all possible orders and the word so formed are arranged in a dictionary order, then find the rank of word ‘MOTHER’?

Using the digits 1, 2, 3, 4, 5, 6,7. how many 3 digits even numbers can be made, no digit being repeated?

From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?