GATE CSE 1990 | Question: 3-ix

Question

The number of ways in which $5\; A's, 5\; B's$ and $5\; C's$ can be arranged in a row is:

• A. $15!/(5!)^{3}$
• B. $15!$
• C. $\left(\frac{15}{5}\right)$
• D. $15!(5!3!)$.

Comments

why there’s a multi-select tag?

Answer 1

(A) Use permutation with repetitions formula as we have to arrange $15$ elements where $5$ each are identical. 

Comments

https://brilliant.org/wiki/permutations-with-repetition/

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Permutation with constrained repetitions:

Number of permutations of n-objects in which

q1 are of same type

q2 are of same type

.

.

$=\dfrac{n!}{q1!\ q2!\ q3!...qn!}$

Answer 2

The longer way

Option  $\large A$