(A) The word $UNIVERSAL$ contains $9$ distinct letters: $U, N, I, V, E, R, S, A, L$.To form a $3$-letter word,we need to select and arrange $3$ letter

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) The word $UNIVERSAL$ contains $9$ distinct letters: $U, N, I, V, E, R, S, A, L$.To form a $3$-letter word,we need to select and arrange $3$ letters out of $9$.The number of ways to arrange $r$ objects out of $n$ distinct objects is given by the permutation formula $P(n, r) = \frac{n!}{(n-r)!}$.Here,$n = 9$ and $r = 3$.Number of words $= P(9, 3) = 9 \times 8 \times 7 = 504$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Difficult

How many words can be formed using any $3$ letters from the word $UNIVERSAL$?

A
$504$
B
$405$
C
$540$
D
$450$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Permutation and Combination

Subtopic

Definition of permutation, Number of permutations with or without repetition, Conditional permutations

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits such that the odd digits occupy even places?

MediumIIT 2000

View Solution

How many numbers lying between $100$ and $1000$ can be formed with the digits $0, 1, 2, 3, 4, 5$,if the repetition of the digits is not allowed?

Easy

View Solution

Find the number of permutations of the letters of the word $ALLAHABAD$.

Easy

View Solution

How many numbers less than $1000$ can be formed using the digits $1, 2, 3, 4, 5, 6$ if repetition is not allowed?

Medium

View Solution

How many $6$-digit numbers can be formed using the digits of the number $112233$?

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

How many words can be formed using any $3$ letters from the word $UNIVERSAL$?

Similar Questions

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits such that the odd digits occupy even places?

How many numbers lying between $100$ and $1000$ can be formed with the digits $0, 1, 2, 3, 4, 5$,if the repetition of the digits is not allowed?

Find the number of permutations of the letters of the word $ALLAHABAD$.

How many numbers less than $1000$ can be formed using the digits $1, 2, 3, 4, 5, 6$ if repetition is not allowed?

How many $6$-digit numbers can be formed using the digits of the number $112233$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module