How many words, with or without meaning, can be formed by selecting $3$ consonants and $2$ vowels from $7$ consonants and $4$ vowels?

Question

There are $7$ consonants and $4$ vowels. How many words, with or without meaning, can be formed by selecting $3$ consonants and $2$ vowels? Should one consider permutation or combination?

These are permutations. – N. F. Taussig Mar 13 '16 at 12:15 — N. F. Taussig, Mar 13 '16 at 12:15

score 1 · Answer 1 · answered Mar 13 '16 at 12:15

How many words can be formed by selecting $3$ consonants and $2$ vowels?

Assuming that each letter is unique and selected without replacement:

$$\binom73\cdot\binom42\cdot(3+2)!$$

Should one consider permutation or combination?

As you can understand from the "$(3+2)!$" in the previous answer: permutation.

How many words, with or without meaning, can be formed by selecting $3$ consonants and $2$ vowels from $7$ consonants and $4$ vowels?

1 Answers1