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

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

Guest Feb 5, 2015

#2
+85624
+5

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..!!!

CPhill  Feb 5, 2015
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#1
+92191
+5

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  Feb 5, 2015
#2
+85624
+5

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..!!!

CPhill  Feb 5, 2015
#3
+85624
0

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