Practice Permutation and combination Questions and Answers

• Find the number of words that can be formed by using all letters of the word 'LAPTOP', if order of vowels remains same.
• Find the number of words that can be formed by using all letters of the word 'PAINT', if order of vowels remains same.
• In how many different ways can the letters of the word ‘FLOWER’ be arranged in such a way that the vowels occupy only the odd positions?
• In how many different ways can the letters of the word ‘NATURE’ be arranged in such a way that the vowels occupy only the odd positions?
• In how many different ways can the letters of the word ‘PUBLIC’ be arranged in such a way that the vowels occupy only the odd positions?
• In how many ways can 4 boys and 3 girls can be seated in a row so that they are in alternate position.
• In how many ways can 3 boys and 2 girls can be seated in a row so that they are in alternate position.
• In how many ways can 6 boys and 3 girls can be seated in a row so that they are in alternate position.
• In how many ways can 7 boys and 2 girls can be seated in a row so that they are in alternate position.
• In how many different ways can the letters of word ‘PUMPKIN’ be arranged?
• In how many ways can the letters of the word ‘MEDICAL’ be rearranged so that the vowels never come together?
• A box contains 2 blue, 3 black and 5 orange balls. In how many ways can 3 balls be drawn from the box, if at least 1 black ball is to be included in the dr...
• Find the quantity of arrangements of the letters of the word INDEPENDENCE if all the vowels always occur together?
• Find the quantity of methods of picking 4 cards from a set of 52 playing cards if four cards are of the same unit? ...
• Which of the following is TRUE for “complementary event or ‘not event’”?
• What will be the number of permutations of n different things, taken r at a time, where repeatition is allowed?
• Find the number of words that can be formed by using all letters of the word 'TANGLE', if it starts with letter G and end with letter A.
• How many different ways can the letters of the word ‘DEMONETIZATION’ be arranged?
• How many ways can 8 women and 8 men be seated around a circular table where no two women can sit together?
• 7 children are to be selected from a group of 8 boys and 6 girls. In how many ways will the children with at most 3 girls and at least 4 boys be selected?
• In How many ways can a student choose a program of 5 courses, if 9 courses are available and 2 courses are compulsory for every student?
• 11 people decided to spend an afternoon in two groups. A group of them decided to go to the theater and the remaining decided to play tennis. In how many w...
• 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?
• 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...
• In how many ways, can a team of 11 players be selected from a squad of 16 players? 
• 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...