How many ways can Pete, Mary, Sue, and Joe stand in a line if Joe and - ProProfs Discuss
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How many ways can Pete, Mary, Sue, and Joe stand in a line if Joe and Sue cannot stand next to each other?

Asked by Wyatt Williams, Last updated: Aug 10, 2021

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De Caevel

De Caevel

De Caevel
De Caevel

Answered Oct 02, 2017

12, cause the solutions where you invert M and P are also to exclude (SJMP, MSJP, MPSJ, JSMP, MJSP and MPJS are also to exclude)

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Wyatt Williams

Wyatt Williams

Wyatt Williams
Wyatt Williams

Answered Sep 12, 2017

18

The strategy here is to count: Number of ways = Total number of ways that PMSJ can stand together - Number of ways that SJ stand next to eachother The total number of ways that PMSJ can stand next to each other is equal to 4! = 4*3*2*1 = 24. The number of ways that SJ will end up standing next to eachother is 6: (SJPM, PSJM, PMSJ, JSPM, PJSM, PMJS) So, 24 - 6 = 18 ways.
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