there are 5 distinct letter,,,,,,,,in which 1E,2A,1S,2Y,1W
Selected 4 letters can have following 3 patterns:
a)abcd (all four letter are different) :
5P4 =120(choosing 4 distinct letters out of 5, when order matters)
b)aabc (from 4 letters 2 are the same and other 2 are different) :
2C1 * 4C2 * 4!/2! = 48
here choosing 2C1, becoz we want "aa" type(out of 2 double letter - AY)
4C2 choosing for third and fourth letters out of 4 distinct letters left
and multiplying by 4!/2! to get different arrangement (for example AABC can be arranged in 4!/2! way)
c) aabb (from 4 letters 2 are the same and other 2 are also the same) :
2C2 * 4!/2! 2! = 6
here 2C2 choosing which two double letter will provide two letters (out of 2 double letter - AY)
and multiplying by 4!/2! 2! to get different arrangement.
120 + 48 +6 = 174 ways
