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Bunuel
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A class of 30 students take up a full row at a movie theater. If there 27 Jan 2022, 03:05
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45% (medium)

Question Stats:

61% (01:29) correct 39% (01:57) wrong based on 253 sessions

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A class of 30 students take up a full row at a movie theater. If there are six couples among the students and if each couple wants to sit together, in how many different ways can the students sit?

A. \(24!*6\)

B. \(24!*12\)

C. \(24!*2^6\)

D. \(25!*6!\)

E. \(24!*6!*2^6\)


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Bunuel
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A class of 30 students take up a full row at a movie theater. If there 04 Feb 2022, 03:15
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Bunuel
A class of 30 students take up a full row at a movie theater. If there are six couples among the students and if each couple wants to sit together, in how many different ways can the students sit?

A. \(24!*6\)

B. \(24!*12\)

C. \(24!*2^6\)

D. \(25!*6!\)

E. \(24!*6!*2^6\)



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Number the students from 1 through 30.

Glue couples together: {1, 2}, {3, 4}, {5, 6}, {7, 8}, {9, 10}, {11, 12}.

We'd be left with 30 - 12 = 18 single students and together with couples' units we'd get 6 + 18 = 24 units: {1, 2}, {3, 4}, {5, 6}, {7, 8}, {9, 10}, {11, 12}, {13}, {14}, {15}, ..., {30}.

These 24 units can be arranged in 24! ways. Each couple within their unit can be additionally arranged in 2! ways (for example, {1, 2} or {2, 1}).

Therefore the final answer is \(24!*(2*2*2*2*2*2)= 24!*2^6\).

Answer: C.
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A class of 30 students take up a full row at a movie theater. If there 27 Jan 2022, 03:22
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Bunuel
A class of 30 students take up a full row at a movie theater. If there are six couples among the students and if each couple wants to sit together, in how many different ways can the students sit?

A. \(24!*6\)

B. \(24!*12\)

C. \(24!*2^6\)

D. \(25!*6!\)

E. \(24!*6!*2^6\)



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Suppose couples are single people. Then number of ways in which they will sit is 24!

Now each couple can sit in 2 way. There are six couples. 2^6

Total no of ways = 24!x2^6

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A class of 30 students take up a full row at a movie theater. If there 04 May 2025, 21:31
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A class of 30 students take up a full row at a movie theater. If there are six couples among the students and if each couple wants to sit together, in how many different ways can the students sit?

30 students

6 couples

6 couples = 12 students

30 - 12 = 18 single students

First arrange the couples and single students.

Since each couple sits together, each couple becomes 1 element in the arrangement.

Since there are 6 couples and 18 single students, there are 24 elements to be arranged.

Ways to Arrange 24 Elements = 24!

Then, within each arrangement of 24 elements, there are 2 ways to arrange each of the 6 couples.

Ways to Arrange the Couples Within Each Arrangement of 24 Elements = \(2^6\)

Total Number of Arrangements = \(24!*2^6\)

A. \(24!*6\)

B. \(24!*12\)

C. \(24!*2^6\)

D. \(25!*6!\)

E. \(24!*6!*2^6\)

Correct answer: C
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