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Permutations (Did I do this correctly)?
Alfonso, Derek, Jason, Bernie, and Travis are the first five batters on the line up card for a baseball game. In how many ways can the card be completed if Travis will not bat right before or after Alfonso?
This is what I did:
5! - 3! = 114
Is that right? Total number of possibilities minus the possibilities where Travis can bat?
You have to deal with Travis and Alfonso.
You have 5 cases:
1) Alfonzo bats first, so Travis cannot bat second
P = 3 * 3 * 2 * 1 (three guys can bat second, three left to bat, 2 left, 1 left )
2) Alfonzo bats second, so Travis cannot bat first or third
P = 3 * 2 * 2 * 1
3) Alfonzo bats third, so Travis cannot bat second or fourth
P = 4 * 2 * 1 * 1
P = 1 * 3 * 2 * 1 (Travis bats first) + 3 * 2 * 1 * 1 (Travis bats fifth)
4) Alfonzo bats fourth, so Travis cannot bat third or fifth
P = 3 * 2 * 2 * 1 (same as batting 2nd)
5) Alfonzo bats fifth, so Travis cannot bat fourth
P = 3 * 3 * 2 * 1 ( same as batting first)
Baseball Equipment & Skills : How to Choose a Baseball Bat for Little Leaguers