How many different words can be formed with the letters BBCCD (not necessarily meaningful words)?

3780 different words

Step-by-step explanation:

The number of possible words that can be formed by a word with n letters is given by n! (factorial of n), but when we have repeated letters, we need to divide the result by the factorial of each number of repeated letters.

In this case, we have 9 letters, but we have 4 times A, 2 times B and 2 times C, so the formula to calculate the number of different words is:

So we can form 3780 different words.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4