Permutations & Combinations — practice questions, page 5
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From 5 different pairs of shoes, 4 shoes are picked at random. In how many ways can this be done…How many solutions in positive integers does x+y+z=12 have?Five different balls are put into 3 different boxes so that no box is empty. In how many ways can…In how many arrangements of the letters of ARRANGE do the two R's NOT come together?All arrangements of the letters of KANPUR are written in dictionary order. What is the position of…Three friends sit in a row of 10 chairs so that no two of them are in neighbouring chairs. In how…A 6 × 6 board of squares is shown. How many rectangles drawn along its lines are NOT squares?A committee of 5 is to be chosen from 6 married couples so that no husband and wife are both on…How many 4-digit numbers have digits that add up to 10?In the triangle shown, 3 points are marked on side AB, 4 on side BC and 5 on side CA (none at a…Every 4-digit number that uses each of the digits 0, 1, 2 and 3 exactly once is written down. What…In how many arrangements of the letters of BANANA are the two N's not next to each other?On the grid shown, moves are only right or up from A to B. How many shortest routes pass through P…Ten identical balls are placed in 4 different boxes so that no box holds more than 4 balls (a box…Two squares of an 8 × 8 chessboard are chosen so that they share a common side. In how many ways…How many 2-digit numbers have two different digits?A bus has 7 empty seats when 2 passengers board. In how many ways can the two of them sit?A mobile PIN has 4 digits from 0 to 9, and digits may repeat. How many PINs are possible?One boy and one girl are to lead the morning assembly. The class has 8 boys and 6 girls. How many…Seven points are marked on a circle as shown. How many chords can be drawn joining two of these…A red die, a blue die and a green die are rolled together. How many different outcomes are possible?Pooja has 3 different hair bands and 4 different hair clips. She wears just one item in her hair…Two-letter arrangements (no letter repeated) are made from the letters of INDORE. How many are…Count the distinct arrangements of the letters of TOMATO.Four-digit numbers are formed from the digits 1 to 7 with no digit repeated. How many of them…
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