Permutations & Combinations — practice questions with answers
211 questions with worked solutions. Open any question to see the full step-by-step answer.
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A captain and a vice-captain are to be chosen from a squad of 11 cricketers. In how many ways can…How many different arrangements can be made using all the letters shown in the figure?How many 3-digit even numbers can be formed from the digits 1 to 6 if no digit is repeated?Six family members sit around the circular dining table shown. In how many different ways can they…How many diagonals does the 10-sided polygon in the figure have?How many triangles can be drawn with their corners at the points marked on the circle in the figure?From the groups in the figure, a committee of 3 men and 2 women is to be chosen. In how many ways…A fruit seller has one each of 5 different fruits. In how many ways can a customer buy at least…Arun says the number of ways to choose 2 class monitors (with the same duties) from 30 students is…A team of 4 is chosen from 9 employees, and Mr. Gupta must be in the team. How many teams are…In a league of 10 teams, every team plays every other team twice (home and away). How many matches…Using the digit cards in the figure without repetition, how many 4-digit numbers can be formed?How many different necklaces can be made from 7 beads of different colours?In the street grid shown, how many shortest routes are there from A to B?A committee of 4 is to be formed from 5 men and 3 women. In how many ways can it be formed if it…In how many ways can the letters of PLANET be arranged so that the two vowels are always together?A bag has the balls shown in the figure. In how many ways can 2 balls of different colours be…In how many ways can 5 boys and 3 girls stand in a row if the 3 girls must stand together?From 8 people, a group of 3 is selected. Two of them, Asha and Bela, refuse to be in the group…From the balls in the figure, 3 are drawn. In how many ways can the draw contain at least 2 red…Seven people sit at a round table. In how many ways can they be seated if two particular people,…Six different storybooks are to be shared equally between two sisters, Diya and Nisha. In how many…There are 10 points in a plane, of which exactly 4 lie on one straight line and no other three are…In the grid shown, how many shortest routes from A to B pass through the point C?In how many arrangements of the letters of ORANGE are the three vowels NOT all together?
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