Permutations and Combinations (p-2) Maths (commerce) - Permutations and Combinations (p-2)

A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.

Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.

Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.

How many words can be formed by writing letters in the word CROWN in a different order?

Thane is the 20th station from C.S.T. If a passenger can purchase a ticket from any station to any other station, how many different tickets must be available at the booking window?

Find the number of words that can be formed by using all the letters in the word REMAIN. If these words are written in dictionary order, what will be the 40th word?

Five balls are to be placed in three boxes, where each box can contain upto five balls. Find the number of ways if no box is to remain empty.

After a meeting, every participant shakeshands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.

A code word is formed by two distinct English letters followed by two non-zero distinct digits. Find the number of such code words. Also, find the number of such code words that end with an even digit.

How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits
(i) are allowed
(ii) are not allowed

How many five-digit numbers formed using the digit 0, 1, 2, 3, 4, 5 are divisible by 3 if digits are not repeated?