How many anagrams can be made from the phrase "Apple pizza" if the "L" has to be followed by an a, e, or i?
I think there there are P(10: 3,2,2,1,1,1) = 10! / (3! * 2! * 2!) anagrams without the L restriction. Any help with how to factor in the L restriction would be appreciated.
Thanks!
Makes sense. We act as if there are 9 letters, one of which is the letter 'la', 'li', or 'le'
CaseI is where the 9th letter is 'la', CaseII is where it is 'le' or 'li'. Case 1 does not have a second 2! because 'la' and 'a' are different letters. So solutions is: CaseI + 2*CaseII
Hello, Sox!
I have a slightly different answer . . .
How many anagrams can be made from the phrase "APPLE PIZZA"
if the has to be followed by an ?
We have 10 letters with some repetition: .
We have three cases to consider . . .
,Duct-tape together.
. . . .Then we have 9 "letters" to arrange: .
. . . .There are: . possible anagrams.
.Duct-tape together.
. . . .Then we have 9 "letters" to arrange: .
. . . .There are: . possible anagrams.
.Duct-tape together.
. . . .Then we have 9 "letters" to arrange: .
. . . .There are: . possible anagrams.
. . . .But in each of these anagrams, the two 's can be switched.
. . . . . without creating a new anagram.
. . . .Our count is too large by a factor of 2.
. . . .There are: . anagrams for this case.
Got it?
Thanks for the response.
"But in each of these anagrams, the two 's can be switched without creating a new anagram. Our count is too large by a factor of 2."
I don't think this is correct. I think we need to act like there is only one A, the other is an "LA". These are two entirely different letters. You can't just switch A with A, you would have to switch A with "LA". So the third case would be as 9! / (3! * 2!)