Permutations & Combinations — practice questions, page 7
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QuestionA basket has 4 identical apples, 5 identical mangoes and 3 different oranges. In how many ways can…QuestionSix people sit at a round table, and Amit must sit directly opposite Bina. How many seatings are…QuestionThe product of the three digits of a 3-digit number is 12. How many such numbers are there?QuestionThree of the 12 corners of the regular 12-sided polygon shown are joined to form a triangle. How…QuestionHow many 4-letter arrangements can be made from the letters of PARALLEL?QuestionIn how many ways can 10 be written as an ordered sum of positive whole numbers (for example 3+7…QuestionThe arrangements of the letters of MUMBAI are listed in dictionary order. In which position does…QuestionUsing the digits 0, 1, 2, 3, 4 and 5 with no repetition, how many 4-digit numbers divisible by 3…QuestionSix different books are given to 3 students so that every student gets at least one book. In how…QuestionThree different numbers are chosen from 1, 2, 3, …, 20. In how many ways can they be chosen so…QuestionHow many 4-digit numbers contain the digit 5 exactly once?QuestionSix identical marbles are put into 3 identical boxes, and boxes may be empty. In how many ways can…QuestionFind the number of arrangements of the letters of ARRANGEMENT.QuestionHow many squares of all sizes can be traced along the lines of the 5 × 4 grid of unit squares shown?QuestionSix couples meet at a party. Everyone shakes hands once with every other person except his or her…QuestionAn art contest has 10 entries. The judge awards a first prize and a second prize to two different…QuestionA museum has 6 gates. Gopal enters by one gate and leaves by any gate, possibly the same one. In…QuestionA display has 3 lamps in a row, and each lamp can glow red, yellow or blue. Every lamp must glow.…QuestionTwo different prizes are given to 2 of the 6 finalists of a debate, one prize each. In how many…QuestionA hockey team plays 5 matches, and each match ends in a win, a loss or a draw. How many different…QuestionA true-or-false test has 10 questions. In how many ways can a student answer every question so…QuestionA diner offers 4 soups and 6 kinds of bread. Vikram orders one soup and two different kinds of…QuestionHow many 4-digit numbers have all four digits even?QuestionFive identical saffron flags and three identical white flags are hung in a row. How many different…QuestionEight teams play a league in which every pair meets once. The top 4 then play two semi-finals, a…
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