Permutations and Combinations
What is the value of $5!$ (5 factorial)?
Evaluate $^5P_2$.
Evaluate $^6C_4$.
If $^nC_8 = ^nC_2$, find the value of $n$.
What is the value of $0!$?
If $^nP_4 = 30 \times ^nP_2$, find the value of $n$.
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4, and 5 assuming that repetition of the digits is not allowed?
In how many ways can a committee of 3 persons be chosen out of 8 persons?
How many words can be formed using all the letters of the word 'ROSE'?
Find the number of arrangements of the letters of the word 'ALLAHABAD'.
What is the value of $^nC_n$?
What is the value of $^nC_0$?
If $^nP_r = 720$ and $^nC_r = 120$, find the value of $r$.
How many chords can be drawn through 21 points on a circle?
If there are 4 routes from Delhi to Jaipur and 3 routes from Jaipur to Mumbai, how many different routes are there from Delhi to Jaipur to Mumbai?
What is the identity for $^nC_r + ^nC_{r-1}$?
Out of 5 men and 2 women, a committee of 3 members is to be formed. In how many ways can it be formed if the committee contains at least one woman?
Find the number of words with or without meaning which can be made using all the letters of the word 'AGAIN'.
If $^nC_{12} = ^nC_8$, find the value of $^nC_2$.
What is the value of $^{5}P_{2}$?
What is the value of $^{5}C_{2}$?
If $^{n}C_{9} = ^{n}C_{8}$, then the value of $n$ is:
In how many ways can the letters of the word 'ROSE' be arranged?
How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition?
What is the number of diagonals of an $n$-sided polygon?
If $^{n}C_{r} + ^{n}C_{r-1}$ is equal to:
Find the number of ways of selecting 4 cards from a pack of 52 playing cards.
If $^{n}C_{8} = ^{n}C_{2}$, then find the value of $^{n}C_{3}$.
In how many ways can 5 people sit around a circular table?
If $\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}$, find the value of $x$.
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done?
How many words (with or without meaning) can be formed using all the letters of the word 'DAUGHTER'?
If $^{n}P_{r} = 840$ and $^{n}C_{r} = 35$, find the value of $r$.
Find the number of ways of arranging the letters of the word 'INDEPENDENCE'.