(B) The total number of letters is $6$ $(a, b, c, d, e, f)$. The vowels are $a, e$ ($2$ vowels) and the consonants are $b, c, d, f$ ($4$ consonants).T

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

(B) The total number of letters is $6$ $(a, b, c, d, e, f)$. The vowels are $a, e$ ($2$ vowels) and the consonants are $b, c, d, f$ ($4$ consonants).Total arrangements of $3$ letters from $6$ letters without repetition is $^6P_3 = 6 \times 5 \times 4 = 120$.Arrangements with no vowels (i.e.,all $3$ letters are consonants) is $^4P_3 = 4 \times 3 \times 2 = 24$.Therefore,the number of arrangements with at least one vowel is $120 - 24 = 96$.

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

Medium

How many arrangements of $3$ letters can be made from the letters $a, b, c, d, e, f$ without repetition,such that each arrangement contains at least one vowel?

A
$72$
B
$96$
C
$24$
D
$128$

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

All the letters of the word $ABRACADABRA$ are arranged in different possible ways. The number of such arrangements in which the vowels are together is:

DifficultMHT CET 2021

View Solution

$A$ vehicle registration number consists of $2$ letters of the English alphabet followed by $4$ digits, where the first digit is not zero. The total number of vehicles with distinct registration numbers is

EasyWBJEE 2012

View Solution

How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

EasyAP EAMCET 2022

View Solution

Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

DifficultJEE MAIN 2025

View Solution

In how many ways can $6$ people be arranged in a row such that $A, B, C,$ and $D$ always appear in the order $ABCD$ (not necessarily together)?

Difficult

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 arrangements of $3$ letters can be made from the letters $a, b, c, d, e, f$ without repetition,such that each arrangement contains at least one vowel?

Similar Questions

All the letters of the word $ABRACADABRA$ are arranged in different possible ways. The number of such arrangements in which the vowels are together is:

$A$ vehicle registration number consists of $2$ letters of the English alphabet followed by $4$ digits, where the first digit is not zero. The total number of vehicles with distinct registration numbers is

How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

In how many ways can $6$ people be arranged in a row such that $A, B, C,$ and $D$ always appear in the order $ABCD$ (not necessarily together)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module