In how many ways can the letters of the word banana be rearranged such that the new word does not begin with a b?

First arrange the words in order:

AAABNN

so there are 3 A's, 1 B and 2 N's.

If there were no constraints,

Number of permutations = (3+1+2)!/(3!1!2!)=6!/(6*1*2)=720/(6*2)=60

Number of words that begin with B is to take out the B, that leaves us with

AAANN => 3 A's and 2 N's

=> 5!/(3!2!) = 120/(6*2)=10

Therefore the number of words that do NOT begin with B is

60-10 = 50 ways

the line of

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)