CUET General Test Quantitative Reasoning > Permutation & Combination PYQs

In how many different ways can the letters of the word 'RUMOUR' be arranged?

In how many different ways can the word "DAUGHTER" be arranged so that the vowels always come together?

How many ways can 10 persons shake hands with two persons?

In how many different ways can the letters of the word 'DELETE' be arranged?

In how many different ways can the letters of the word 'OFFICE' be arranged so that the vowels never come together?

In how many different ways can the letters of the word 'DELETE' be arranged?

In how many different ways, can the letters of the word ASSOCIATION be arranged, so that the vowels always come together?

How many ways, can the letters of the word 'QUANTITATIVE' be arranged, so that all T are together?

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

Match List-I with List-II | List-I | List-II | |---|---| | (A) $^n{C_{r-1}} + ^n{C_r}$ | (I) $^n{C_{n-r}}$ | | (B) $^n{C_r}$ | (II) $n + ^1{C_r}$ | | (C) $^{50}{C_r} = ^{50}{C_{r+2}}$, then r = | (III) 24 | | (D) $^n{P_3} = 9240$, n=? | (IV) 22 | Choose the correct answer from the options given below:

In a plane, there are 9 points, out of which 4 are collinear. The number of triangles made by these points is:

Match List-I with List-II | List-I | List-II | |---|---| | (A) $^{75}P_2 - ^{75}C_2$ | (I) 504 | | (B) $^{5}P_5 - ^{10}C_3$ | (II) 6 | | (C) $^{16}C_{13} - ^{8}C_3$ | (III) 2775 | | (D) $^nP_4 = 360$, then find n | (IV) 0 | Choose the correct answer from the options given below:

Out of 6 men and 4 women, a committee of 5 members is to be formed so that it has 2 women and 3 men. In how many different ways can it be done:

How many ways can a committee of 3 people be chosen out of 7 people?

In how many ways are the letters of the word DOCUMENT arranged so that all the vowels always come together?

Match List-I with List-II | List-I | List-II | |---|---| | (Expressions) | (Values) | | (A) 1/6! + 1/7! = x/8! Find x | (I) 1 | | (B) Evaluate: $\frac{n!}{(n-r)!}$, n = 6, r = 2 | (II) 100 | | (C) If ⁿC₉ = ⁿC₈, find ⁿC₁₇. | (III) 64 | | (D) ⁶P₃ - ⁵P₂ | (IV) 30 | Choose the correct answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | (Expression) | (Value) | | (A) $\frac{12!}{10!(2!)}$ | (I) 110 | | (B) $^nC_2 = 210$, find n. | (II) 136 | | (C) $^6P_3 - ^5C_2$ | (III) 66 | | (D) If $^nC_9 = ^nC_8$, find $^nC_{15}$ | (IV) 21 | Choose the correct answer from the options given below:

In a team every player shakes his hand with other player only once. If total number of handshakes is 120, then the number of players is:

Match List-I with List-II | List-I | List-II | |---|---| | (A) The number of different words that can be formed with CUSTOM with the condition that the word should begin with M is ______. | (I) 70 | | (B) The number of different ways in which the letters of the word EXTRA can be arranged so that the vowels are never together is ______. | (II) 45 | | (C) There are 10 points in a plane. No three of these points are in a straight line. The total number of straight line that can be formed by joining the two points is _______. | (III) 72 | | (D) The number of ways a committee of 4 people be chosen out of 8 people is _______. | (IV) 120 | Choose the correct answer from the options given below:

Match List-I with List-II | List-I | List-II | |---|---| | (Expressions) | (Values) | | (A) $^nP_4 = 360$, then find n | (I) 1155 | | (B) If $^{13}C_{3r} = ^{15}C_{r+3}$, then find r | (II) 56 | | (C) Find $^{15}C_{11} - ^{15}C_4$ | (III) 6 | | (D) Find $^8P_2$ | (IV) 3 | Choose the correct answer from the options given below:

In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?

Five digit numbers formed by using digits 0, 1, 2, 3 and 4 (when repitition of digits are not allowed) are:

Read the information given below carefully and answer the question that follows: (A) The different ways in which the alphabets of the word BAKERY can be arranged is 720 (B) The number of ways in which the alphabets of the word MACHINE can be arranged so that the vowels will occupy only the odd positions is 576 Choose the correct answer from the options given below:

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

There is a match between two teams. Each team has a total of 15 players. After the match, all the players of one team shake hands with all the players of the other team. What is the number of possible hand shakes?

The number of ways a committee consisting of 3 men and 1 women can be formed from 5 men and 3 women, is _________ .

Match List-I with List-II | List-I | List-II | |---|---| | (A) $^8P_3 - ^{10}C_3$ | (I) 6 | | (B) $^8P_5$ | (II) 21 | | (C) $^nP_4 = 360$, then find n. | (III) 216 | | (D) $^nC_2 = 210$, find n. | (IV) 6720 | Choose the correct answer from the options given below:

How many 3-digit even numbers can be formed by using the digits 1 to 9 if no digit is repeated ?

How many 3 digit even numbers can be formed from the digits (0 - 9) if repetition of digits are allowed?