(A) The word $SCHOLAR$ has $7$ distinct letters: $S, C, H, O, L, A, R$.We need to form words starting with $A$ and ending with $S$.Fixing $A$ at the f

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

(A) The word $SCHOLAR$ has $7$ distinct letters: $S, C, H, O, L, A, R$.We need to form words starting with $A$ and ending with $S$.Fixing $A$ at the first position and $S$ at the last position,we have $5$ remaining letters $(C, H, O, L, R)$ to arrange in the $5$ middle positions.The number of ways to arrange these $5$ letters is $5!$.$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$.Therefore,$120$ such words can be formed.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Easy

How many words can be formed using the letters of the word $SCHOLAR$ that start with $A$ and end with $S$?

A
$120$
B
$720$
C
$1440$
D
$5040$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Permutations and Combinations

Subtopic

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

Assuming that no two consecutive digits are same,the number of $n$-digit numbers is:

Difficult

View Solution

The number of permutations by taking all letters and keeping the vowels of the word $COMBINE$ in the odd places is

MediumWBJEE 2010

View Solution

$10$ men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

DifficultAP EAMCET 2013

View Solution

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?

Medium

View Solution

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.

Medium

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 the letters of the word $SCHOLAR$ that start with $A$ and end with $S$?

Similar Questions

Assuming that no two consecutive digits are same,the number of $n$-digit numbers is:

The number of permutations by taking all letters and keeping the vowels of the word $COMBINE$ in the odd places is

$10$ men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

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?

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.

Vedclass Test Series

Exam Paper Generator

Online Exam Module