Permutations and Combinations Practice Questions - Level 1

How many numbers of 3-digits can be formed with the digits 1, 2, 3, 4, 5 (repetition of digits not allowed)?

How many numbers between 2000 and 3000 can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7 (repetition of digits not allowed)?

In how many ways can a person send invitation cards to 6 of his friends if he has four servants to distribute the cards?

In how many ways can 5 prizes be distributed to 8 students if each student can get any number of prizes?

In how many ways can 7 Indians, 5 Pakistanis and 6 Dutch be seated in a row so that all persons of the same nationality sit together?

There are 5 routes to go from Allahabad to Patna & 4 ways to go from Patna to Kolkata, then how many ways are possible for going from Allahabad to Kolkata via Patna?

There are 4 qualifying examinations to enter into Oxford University: RAT, BAT, SAT, and PAT. An Engineer cannot go to Oxford University through BAT or SAT. A CA on the other hand can go to the Oxford University through the RAT, BAT & PAT but not through SAT. Further there are 3 ways to become a CA (viz., Foundation, Inter & Final). Find the ratio of number of ways in which an Engineer can make it to Oxford University to the number of ways a CA can make it to Oxford University.

How many straight lines can be formed from 8 non-collinear points on the X-Y plane?

 If ${}^{n}C_{3} = {}^{n}C_{8}$, find $n$.

In how many ways can the letters of the word DELHI be arranged?