Practice Permutation and combination Questions and Answers

• A group consists of 7 boys and 12 girls. In how many ways can 3 boys and 5 girls be selected from the group?
• A group consists of 10 boys and 6 girls. In how many ways can 6 boys and 2 girls be selected from the group?
• A group consists of 11 boys and 9 girls. In how many ways can 7 boys and 5 girls be selected from the group?
• A group consists of 6 boys and 8 girls. In how many ways can 2 boys and 3 girls be selected from the group?
• A group consists of 12 boys and 7 girls. In how many ways can 5 boys and 3 girls be selected from the group?
• A group consists of 10 boys and 10 girls. In how many ways can 6 boys and 4 girls be selected from the group?
• A group consists of 8 boys and 6 girls. In how many ways can 4 boys and 2 girls be selected from the group?
• A group consists of 9 boys and 8 girls. In how many ways can 3 boys and 5 girls be selected from the group?
• Seven books out of which 4 are novels and rest are comics have to be arranged on a shelf. Find the number of ways of arrangement in which all four novels a...
• Six people out of which 3 are brothers and the rest are strangers are to be seated in a row. Find the number of ways in which all three brothers are not si...
• Seven balls out of which 4 are red and the rest are green are to be arranged in a row. Find the number of arrangements in which all four red balls are not ...
• Five toys out of which 2 are identical robots and the rest are different action figures are to be arranged in a row. Find the number of arrangements in whi...
• Seven musicians out of which 3 are from the same band and the rest are solo artists are to be seated in a row. Find the number of ways in which the three b...
• Eight books out of which 4 are part of a series and the remaining are standalone books are to be arranged on a shelf. Find the number of arrangements in wh...
• Five articles out of which 3 are cups and rest are glasses have to be arranged on a shelf. Find the number of ways of arrangement in which all three cups a...
• Five different pens out of which 2 are red and the rest are blue are to be arranged in a line. Find the number of ways in which the two red pens are not pl...
• Eight dancers out of which 3 are from the same team and the rest are solo performers have to perform in a sequence. Find the number of sequences in which a...
• A team of 8 players is to be selected from a group of 7 junior players and 6 senior players. In how many ways a team having at least 6 junior players can b...
• From a group of 8 girls and 7 boys, a committee of 9 is to be formed. In how many ways can the committee be formed if it must include at least 6 girls?
• A team of 10 members is to be formed from 9 engineers and 6 doctors. Find the number of ways the team can be formed with at least 8 engineers.
• From 7 experienced and 4 fresher candidates, a panel of 8 is to be made. How many ways can the panel be formed if it includes at least 6 experienced candid...
• A task force of 9 members is to be selected from a group of 8 male and 6 female officers. In how many ways can a task force be formed if it must contain at...
• From 10 musicians and 5 singers, a band of 8 members is to be formed. In how many ways can the band be formed such that there are at least 6 musicians?
• A team of 7 researchers is to be formed from 6 biologists and 4 chemists. Find the number of ways to form the team if it must include at least 5 biologists...
• In how many ways can a squad of 10 people be selected from 9 trainees and 5 supervisors such that the squad has at least 8 trainees?
• From 7 artists and 6 designers, a team of 9 members is to be selected. In how many ways can this team be formed if it includes at least 6 artists?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "MISTAKE"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "TRIANGLE"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "BALUSTER"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "PAINTER"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "MONARCH"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "CAMPFIRE"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "SEMINAR"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "RECLAIM"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "VINTAGER"?
• How many four-letter words without repetition having exactly two vowels can be formed by using the letters of the word "MEASURE"?
• A team of 6 players is to be selected from 7 men and 5 women. In how many ways can a team be formed such that at least 4 men are included?
• From a group of 8 engineers and 4 doctors, a committee of 6 members is to be formed. Find the number of ways to form the committee such that at least 5 eng...
• A cricket team of 9 players is to be formed from 10 batsmen and 6 bowlers. Find the number of ways to form the team such that at least 7 batsmen are select...
• A school wants to form a committee of 5 students from 6 boys and 4 girls. How many ways can the committee be formed if it must contain at least 3 boys?