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6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, a

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Bunuel
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6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, a [#permalink] New post   23 Jun 2023, 11:00
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6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?

A. 24
B. 36
C. 48
D. 72
E. 144
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Re: 6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, a [#permalink] New post   23 Jun 2023, 15:13
Bunuel wrote:
6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?

A. 24
B. 36
C. 48
D. 72
E. 144


IMO, Option E is the answer.

I temporarily assume abc is temporarily just one person. Therefore, there is 4! = 24 arrangements
However, abc can be arranged within itself in 3! = 6

Therefore, the answer is 4! * 3! = 24 * 6 = 144
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Re: 6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, a [#permalink] New post   23 Jun 2023, 23:43
Bunuel wrote:
6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there

Assuming a,b,c as one element. Hence there are 4! ways.
Also a,b,c can also be lined in 3! ways.

4!*3!=24*6=144
Hence, Opt (E)
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Re: 6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, a [#permalink] New post   24 Jun 2023, 03:09
let abc be X
X DEF
4! ways to arrange them
and DEF can be arranged in 3! ways
4!*3! ; 24*6 ; 144
option E


Bunuel wrote:
6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, and c adhere always together, how many possible cases are there?

A. 24
B. 36
C. 48
D. 72
E. 144
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Re: 6 persons a, b, c, d, e, and f are to be lined up in a row. If a, b, a [#permalink]
24 Jun 2023, 03:09
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