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?

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?

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.