Find the positive integer $n$ such that $\frac{n!}{\left(n-2\right)!}=240$.

Important Questions on Permutations and Combinations

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 8 - Permutations and Combinations>CHAPTER TEST>Q 5

Find $r$ if  ${}^{56}P_{r+6}:{}^{54}P_{r+3}=30800:1$.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 8 - Permutations and Combinations>CHAPTER TEST>Q 6

How many numbers between $20000$ and $30000$ can be formed using the digits $2, 3, 5, 6, 7$ if each digit may be repeated any number of times in any number?

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 8 - Permutations and Combinations>CHAPTER TEST>Q 7

How many words consisting of $2$ vowels and $3$ consonants can be formed from $4$ different vowels and $5$ different consonants?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 8 - Permutations and Combinations>CHAPTER TEST>Q 8

The letters of the word $\mathrm{WIFE}$ are arranged in all possible ways and sorted in dictionary manner. What is the position of the word $\mathrm{WIFE}$ in this arrangement?

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 8 - Permutations and Combinations>CHAPTER TEST>Q 9

How many different words can be formed from the letters of the word $\mathrm{GANESHPURI}$ such that the letter $G$ always occupies the first place?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 8 - Permutations and Combinations>CHAPTER TEST>Q 9

How many different words can be formed from the letters of the word $\mathrm{GANESHPURI}$ such that the vowels are always together?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 8 - Permutations and Combinations>CHAPTER TEST>Q 9

How many different words can be formed from the letters of the word $\mathrm{GANESHPURI}$ such that all consonants come together?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 8 - Permutations and Combinations>CHAPTER TEST>Q 9

How many different words can be formed from the letters of the word $\mathrm{GANESHPURI}$ such that the vowels occupy even places?