Batman vs Superman combined or permuted!
Batman challenged Superman to find the number of permutations of the word 'BATMAN' and Superman challenged Batman to find the position of 'SUPERMAN' in the dictionary made by rearranging its letters. If Batman's answer was and Superman's was , find the value of , assuming both are good in maths!
The answer is 35445.
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For superman:
A _ _ _ _ _ _ _ 7!
E _ _ _ _ _ _ _ 7!
M _ _ _ _ _ _ _ 7!
N _ _ _ _ _ _ _ 7!
P _ _ _ _ _ _ _ 7!
R _ _ _ _ _ _ _ 7!
SA_ _ _ _ _ _ 6!
SE_ _ _ _ _ _ 6!
SM_ _ _ _ _ _ 6!
SN_ _ _ _ _ _ 6!
SP_ _ _ _ _ _ 6!
SR_ _ _ _ _ _ 6!
SUA_ _ _ _ _ 5!
SUE_ _ _ _ _ 5!
SUM_ _ _ _ _ 5!
SUN_ _ _ _ _ 5!
SUPA_ _ _ _ 4!
SUPEA_ _ _ 3!
SUPEM_ _ _ 3!
SUPEN_ _ _ 3!
SUPERA_ _ 2!
SUPERMAN 1
So x = 7 ! × 6 + 6 ! × 6 + 5 ! × 4 + 4 ! + 3 ! × 3 + 2 ! + 1 = 3 5 0 8 5
For Batman:
Number of letters=6, same pair=1. So number of permutations=
y = 2 6 ! = 3 6 0
Required answer= x + y = 3 5 0 8 5 + 3 6 0 = 3 5 4 4 5