How many seating arrangements are possible for 7 girls and 7 boys to sit in a row of 14 seats if no girls can sit next to each other and sit without each other?

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Arvid Rutherford asked a question: How many seating arrangements are possible for 7 girls and 7 boys to sit in a row of 14 seats if no girls can sit next to each other and sit without each other?
Asked By: Arvid Rutherford
Date created: Fri, Jul 23, 2021 12:29 AM
Date updated: Sun, May 15, 2022 8:23 AM

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Top best answers to the question «How many seating arrangements are possible for 7 girls and 7 boys to sit in a row of 14 seats if no girls can sit next to each other and sit without each other»

= 5,040 possible arrangements of the boys.

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Those who are looking for an answer to the question «How many seating arrangements are possible for 7 girls and 7 boys to sit in a row of 14 seats if no girls can sit next to each other and sit without each other?» often ask the following questions:

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  • Expand 2! Expand 4! So 6 choose 4 (where order doesn't matter) yields 15 unique combinations. So there are 15 possible ways that 6 people can sit in 4 chairs.

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😎 How many seating arrangements can 5 people have?

=1*2*3*4*5 =120 ways you can seat 5 people in a row of 5 chairs. So no. Of ways the can be seated=5×4×3×2×1=120. So, 5 people can be seated in 5 seats in 120 ways.

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However, the 7 boys can sit such that no two boys and no two girls sit together even if the seventh chair is at the right end. Thus we have 2 ways in which the chair at the end can be placed. ⇒ The number of ways in which 7 girls and 7 boys can be arranged such that no two boys and no two girls sit together is 7! × 7! × 2 = 5040 × 5040 × 2 = 50803200.

Answer and Explanation: 1. Become a Study.com member to unlock this answer! Create your account. 8 8 boys and 7 7 girls must be seated in a row such that the boys and girls occupy alternate ...

Now 7 gaps are created between these 6 seats. So, we can select any 6 of these 7 gaps and make girls sit there. There are 7C6 * 6! ways to do that (since the girls can shuffle amongst themselves). Hence the total number of ways to make boys and girls sit alternately should be 6! 7C1 * 6! but the answer is 2*6!*6!. What am I missing here?

Click here👆to get an answer to your question ️ In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back? How many seating arrangements are possible if three girls should sit together in a back row on adjacent seats? Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting ...

How many seating arrangements are possible if girls should sit together in a back row on adjacent seats? Join / Login. maths. In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 the back? How many seating arrangements are possible if girls should sit together in a back row on ...

Number of ways in which 7 people can occupy six seats, 3 seats on each side in a first class railway compartment if two specified persons are to be always included and occupy adjacent seats on the same side, is then has the value equal to: 2 (b) 4 (c) 8 (d) None of these

The boys can be arranged first in [math]5![/math]ways. This leaves [math]6[/math] slots between them. The [math]3[/math] girls have to be arranged in these [math]6[/math] places. This can be done in [math]^6P_3[/math] ways. [math]\therefore[/math]...

If we start with the first boy going counterclockwise in the group of 3 boys, and go counterclockwise, we see that there are 7! = 5,040 possible arrangements of the boys. Any of the 3 girls can go in the space between the group of 3 boys and the first group of 2 boys.

With 2 ways to decide if seat number 1 is for a boy or a girls, 24 ways to arrange the boys, and 24 ways to arrange the girls, there are 2*24*24=1152 possible seating arrangements.

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