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12 Nov 2024, 03:09
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Possible pairs: 72
Pairs with Paul's partner: 12
Seven couples attended Shauna’s Online Couple Counseling for a group therapy session during a pandemic. To facilitate a role-playing exercise, Shauna selects one of her 14 clients to demonstrate the activity. She then instructs the remaining attendees to pair up randomly with anyone other than their own partner, leaving one person excluded from the exercise.
If Shauna selects Paul to assist her in demonstrating the activity and then chooses one of the randomly created pairs to role-play with her and Paul, select for Possible pairs the total number of different pairs that can role-play with Shauna and Paul, and select for Pairs with Paul's partner the total number of different pairs that include Paul's original partner and can role-play with Shauna and Paul. Make only two selections, one in each column.
If Shauna selects Paul to assist her in demonstrating the activity and then chooses one of the randomly created pairs to role-play with her and Paul, select for Possible pairs the total number of different pairs that can role-play with Shauna and Paul, and select for Pairs with Paul's partner the total number of different pairs that include Paul's original partner and can role-play with Shauna and Paul. Make only two selections, one in each column.
| Possible pairs | Pairs with Paul's partner | |
| 12 | ||
| 13 | ||
| 14 | ||
| 72 | ||
| 78 | ||
| 780 |
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Official Answer
Possible pairs: 72
Pairs with Paul's partner: 12
12 Nov 2024, 03:09
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Official Solution:
Without Paul, 13 people remain to form pairs. Shauna and Paul can face any two people from these 13, except for 6 pairs that are actual couples among them. Therefore, the total number of different pairs that can role-play with Shauna and Paul is \(C^2_{13} - 6 = 72\).
As for Paul's original partner, that partner can pair with any of the other 12 people, resulting in a total of 12 different pairs that include Paul's original partner.
Correct answer:
Possible pairs "72"
Pairs with Paul's partner "12"
Bunuel
Without Paul, 13 people remain to form pairs. Shauna and Paul can face any two people from these 13, except for 6 pairs that are actual couples among them. Therefore, the total number of different pairs that can role-play with Shauna and Paul is \(C^2_{13} - 6 = 72\).
As for Paul's original partner, that partner can pair with any of the other 12 people, resulting in a total of 12 different pairs that include Paul's original partner.
Correct answer:
Possible pairs "72"
Pairs with Paul's partner "12"
28 Nov 2024, 07:35
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