The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is

Question

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is ________.

Smart Achievers · Accepted Answer

(240)

$The word SYLLABUS consists of$

$2 S, 2 L, 1 Y, 1 A, 1 B, 1 U$

$Required number of ways = {}^{2}C_{1} \times {}^{5}C_{2} \times \frac{4!}{2!}$

$= 2 \times 10 \times 12 = 240$

Solution

Q.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is ________.

Ans.
(240)

$The word SYLLABUS consists of$

$2 S, 2 L, 1 Y, 1 A, 1 B, 1 U$

$Required number of ways = {}^{2}C_{1} \times {}^{5}C_{2} \times \frac{4!}{2!}$

$= 2 \times 10 \times 12 = 240$

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Solution

Q. The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is ________.

Ans. (240) The word SYLLABUS consists of 2S, 2L, 1Y, 1A, 1B, 1U Required number of ways=C12×C25×4!2! =2×10×12=240

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Q.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is ________.

Ans.
(240)

$The word SYLLABUS consists of$

$2 S, 2 L, 1 Y, 1 A, 1 B, 1 U$

$Required number of ways = {}^{2}C_{1} \times {}^{5}C_{2} \times \frac{4!}{2!}$

$= 2 \times 10 \times 12 = 240$