In how many ways could the letters in the word PROBLEM be arranged if the
consonants must remain in the original
order?

There are seven positions to be filled to form 7 letter words using the letters in the word PROBLEM.

Hope this helps!!!

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

13cm

step-by-step explanation:

(apex)