Permutations and Combinations
136 questions· page 1 of 14
How many different colour arrangements are there of the 10 books in which the 3 blue books are together, but the 2 yellow books are not next to each other?
How many different colour arrangements are there of the 10 books with exactly 4 books between the 2 yellow books?
Alissa selects 4 books from her 10 different books from the series Squares and Circles.
Find the number of different selections if the 4 books include at least 1 red book, at most 1 blue book and exactly 1 yellow book.
Find the number of different ways in which the 6 musicians can be selected if there must be at least 3 guitarists, at most 2 pianists and exactly 1 drummer.
Three bands will be selected from the original group of 20 musicians. Each band will consist of 3 guitarists, 1 pianist and 1 drummer. No musician can be in more than one band. The first band selected will play at a concert in France, the second band selected will play in Italy and the third band selected will play in Spain.
Find the number of different ways in which these three bands can be selected.
Find the number of different ways in which the 10 letters in the word AMALGAMATE can be arranged so that there is an M at the beginning, an M at the end and no As are together.
Find the number of different ways in which the 10 letters in the word AMALGAMATE can be arranged with exactly 3 letters between the two Ms.
Five letters are selected from the 10 letters in the word AMALGAMATE.
Find the number of different selections in which the five letters include at least one M and at least two As.
Find the number of different arrangements of the 7 men in a line in which Ali and Ben do not stand next to each other.
Find the number of different arrangements of the 7 men and 4 women in a line in which all the men stand together and all the women stand together.
In how many ways can the 7 men and 4 women be divided into a group of 6, a group of 3 and a group of 2 if there are no restrictions?
The 7 men and 4 women are divided at random into a group of 6, a group of 3 and a group of 2.
Find the probability that Ali, Ben and Charlie are all in the same group.
How many different arrangements are there of the 10 letters in the word SEYCHELLES in which there are exactly two letters between the Ss and one of these two letters is C?
How many different arrangements are there of the 10 letters in the word SEYCHELLES in which there is an S at the beginning, an S at the end and the three Es are not all next to each other?
5 letters are selected at random from the 10 letters in the word SEYCHELLES.
Find the probability that these 5 letters include the three Es.
The Splash Club has 26 members, of whom 16 are swimmers and 10 are divers. No member is both a swimmer and a diver. The club committee consists of 6 of these 26 members.
In how many ways can the club committee be selected if it must include at least 2 swimmers and at least 2 divers?
Find the number of different arrangements of the 9 letters in the word DAFFODILS in which there is a D at each end and the two Fs are not next to each other.
Find the probability that a randomly chosen arrangement of the 9 letters in the word DAFFODILS has exactly 4 letters between the two Ds.
Find the number of different ways in which a team of 6 athletes can be selected if it consists of at least 3 sprinters, at most 2 hurdlers and at most 1 thrower.
A group of 8 athletes chosen from the group of 25 athletes consists of 1 sprinter, 3 hurdlers and 4 throwers. These 8 athletes stand in a row.
How many different arrangements of the 8 athletes are there if the 3 hurdlers do not stand all together?
How many different arrangements of the 8 athletes are there in which there are at least two athletes between any two hurdlers?
In how many ways can the committee of 5 members be chosen if it must include at least 2 men and at least 1 woman?
The 10 members of the club stand in a line for a photograph.
How many different arrangements are there of the 10 members if all the men stand together and all the women stand together?
For a second photograph, the members stand in two rows, with 6 on the back row and 4 on the front row. Olly and his sister Petra are two of the members of the club.
How many different arrangements are there of the 10 members in which Olly and Petra stand next to each other on the front row?
Find the number of different arrangements of the 8 digits in which there is a 2 at the beginning, a 2 at the end and the three 4s are not all together.
Three digits are selected at random from the eight digits 1, 2, 2, 3, 4, 4, 4, 5.
Find the probability that the three digits are all different.