Question

The number of ways of arranging six persons having abcd

Answer 1

The number of ways to arrange ABCD is 4! For each arrangement of ABCD, the number of ways of arranging six persons is same.

Hence, the required number is 6!/4!=30

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Answer 2

There will have $30$ different ways of arranging six persons having $abcd$.

Step-by-step explanation:

Given,

The number of ways of arranging six persons having $abcd$

The number of ways of arranging $abcd=4!$

And,

The number of ways of arranging six persons$=6!$

∴The number of ways of arranging all$=\frac{6!}{4!}$

                                                              $=\frac{6\times 5\times 4!}{4!}$

                                                              $=6\times 5$

                                                             $=30$

So, There will have $30$ different ways of arranging six persons having $abcd$.