three letters from the word planters are chosen, find p(3 consonants)

The total ways we can choose any 3 letters out of 8 is given by C(8,3) = 56

But,we only want to choose 3 of the 6 cosonanats  = C(6,3) = 20

So we have 20 / 56  = 5 / 14  = about a 35.7% chance of choosing a consonant..!!!

planters      plntrs   6 consonants out of 8 letters

P that the first one is  a consonant is 6/8

P that the second one is a consonant is 5/7

P that the 3rd one is a consonant is 4/6

p(all 3 are consonants) =    $${\frac{{\mathtt{6}}}{{\mathtt{8}}}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{5}}}{{\mathtt{7}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{4}}}{{\mathtt{6}}}}\right) = {\frac{{\mathtt{5}}}{{\mathtt{14}}}} = {\mathtt{0.357\: \!142\: \!857\: \!142\: \!857\: \!1}}$$

Melody chose to answer this using a " fundamental counting principle" approach....I chose a "set counting" approach.......again....

"All roads lead to Rome.'

Melody Sorensen (ca. 2015)