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# Consider the word "Calculator"

Tue 6 Sep, 2022 06:50 pm
Consider the word “calculator”.
a.) How many distinct arrangements of the letters are there?
b.) How many distinct arrangements are there if the letter “r” must occur before any of the vowels?

I got 453,600 for part a but am stuck on part b
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engineer

2
Wed 7 Sep, 2022 07:12 am
@D4ng1t,
Work it stepwise. If the first letter is R, how many combinations are there? (This is just like Part A, so 9!/2!/2!/2!). What if the second letter is R? Now you need to do the part in front of the R (just one letter) and the eight letters after the R. Repeat with R in each position and add them up.
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ascribbler

1
Sat 10 Sep, 2022 07:01 am
@D4ng1t,
You could engineer an answer by noting that the letters of 'engineer' have arrangements totalling:

8!/ (3!2!)

https://en.wikipedia.org/wiki/Permutation

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