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

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.