Permutations and Combinations · Basic Numeracy · UPSC Civil Service

Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) ar...

In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots?

There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are ran...

How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even di...

ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn us...

A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements: 1....

What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated?

What is the number of selections of 10 consecutive objects in clockwise direction out of 12 objects arranged in a circle?

In an examination, the maximum marks for each of the four papers namely P, Q, R and S are 100. Marks scored by the students are in integers. A student...

A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in wh...

There are five persons P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assi...

The letters of the word "INCOMPREHENSIBILITIES" are arranged alphabetically in reverse order. How many positions of the letter/letters will remain unc...

The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the n...

How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?

The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. How many such arrangements are possible?

A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A t...

Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition. Cons...

There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to ...

If 15 × 14 × 13 × ... × 3 × 2 × 1 = 3m × n where m and n are positive integers, then what is the maximum value of...

One non-zero digit, one vowel and one consonant from English alphabet (in capital) are to be used in forming passwords, such that each password has to...

There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many...

Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum. Which ...

On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?

Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?

There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons...