all words with 2 distinct vowels and 3 distinct consonants were listed
alphabetically, what would be the rank of “ACDEF’?
The first word would be ABCDE. With 2
distinct vowels, 3 distinct consonants, this is the first word we can come up
Starting with AB, we can have a number
AB __ __ __. The next three slots
should have 2 consonants and one vowel. This can be selected in 20C2
and 4C1 ways. Then the three distinct letters can be
rearranged in 3! Ways.
Or, number of words starting with AB = 20C2
* 4C1 * 3! = 190 * 4 * 6 = 4560
Next, we move on to words starting with
ACB __ __. The last two slots have to
be filled with one vowel and one consonant. = 19C1 * 4C1.
This can be rearranged in 2! Ways.
Or, number of words starting with ACB
= 19C1 * 4C1
* 2 = 19 * 4 * 2 = 152
Next we move on words starting with
ACDB: There are 4 different words on this list – ACDBE, ACDBI, ACDBO, ACDBU
So, far number of words gone = 4560 +
152 + 4 = 4716
After this we move to words starting
with ACDE, the first possible word is ACDEB. After this we have ACDEF.
Labels: CAT Counting, CAT letters and words, CAT Permutation Combination