Practice Permutation and combination Questions and Answers

• A team of 4 men and 2 women is to be selected out of 8 men and 4 women. If only one man and one woman remain in the team, then what will be the total numbe...
• In how many ways can 12 girls be seated in a row of 50 seats so that no girl sits on the adjacent seat? ...
• In an election, a voter can vote for any number of candidates not exceeding the number to be elected. There are 7 candidates and 4 members to be elected. I...
• 6 students appear in an examination. In how many ways can the result be announced?
• How many 6-digit numbers can be formed from the digits 0,3,4,5,6 and 8, in which the digits are not repeated?
• In how many ways will a team of 5 people be selected out of 12 people such that a specific person will always be selected, and a specific person will alway...
• In how many ways can 7 beads be arranged to make a necklace?
• A man has 15 friends out of which 7 are his relatives. In how many ways can he invite his 9 friends in which at least 5 must be his relatives?
• In how many ways can 17 members be seated in two lines with seating capacity of 9 and 8 members respectively? 1.     9! ×8! 2.     17 C9 ×17C8 3....
• How many 5-digit even numbers can be formed using the digits 0 to 9 if no digit is repeated?
• How many three-letter words can be formed such that all letters are vowels, and no two letters are the same?
• How many straight lines can be formed from 9 points out of which 4 are colinear?
• A committee of 4 people is to be formed from a group of 10 individuals. If 2 specific individuals refuse to work together, how many different committees ca...
• Determine the total number of ways to form a committee consisting of 10 members from a pool of 8 men and 7 women, ensuring the committee includes at least ...
• A letter is randomly selected from the word "DETACHMENT." What is the probability that the selected letter is a vowel?
• In how many ways can a committee of 3 men and 2 women be formed from 5 men and 6 women?
• 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...
• A selection of 7 cars must be made from a total of 13 cars for an exhibition. However, one specific car must always be included in the selection. If the ca...
• In how many different ways can the letters of the word "AIRSTRIKE" be arranged if all the vowels must always be grouped together?
• How many unique arrangements can be made using all the letters of the word "DELUSION", ensuring that the vowels do not appear together?
• How many different 10-letter words (with or without meaning) can be formed using all the letters of the word "TEMPTATION"?
• In a bag there are 4 red balls, 3 green balls, and 5 blue balls. If one ball is drawn at random from the bag, what is the probability of drawing a green ba...
• A group consists of 8 boys and 10 girls. In how many ways 5 boys and 4 girls can be chosen from the group?
• A group consists of 9 boys and 7 girls. In how many ways can 4 boys and 3 girls be selected from the group?
• 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...