Miss_Hickey
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- Dec 28, 2017
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I am a high school Maths teacher seeking help with permutations and combinations. My question is:
Three letters are chosen at random from the word BANANA SPLIT. What is the probability that they are all consonants?
The worked solution uses combinations as follows:
There are 11 letters and 7 consonants.
consonant combinations = 7C3
= 7!/{3!(7-4)!}
= 35
total combinations = 11C3
= 11!/{3!(11-3)!}
P(all consonants) = 35/165
= 7/33
I understand all of the steps, except for why combinations is chosen rather than permutations. It is my understanding that combinations are used when the order of choices does not matter. However, in probability the order would matter - for example, the choice of SPL from the letters should be counted along with PSL, PLS, SLP etc.
When I calculated the example using permutations, I did not get 7/33:
consonant permutations = 7P3
total permutations = 11P3
P(all consonants) = 840 / 6 652 800
Thank you!
Three letters are chosen at random from the word BANANA SPLIT. What is the probability that they are all consonants?
The worked solution uses combinations as follows:
There are 11 letters and 7 consonants.
consonant combinations = 7C3
= 7!/{3!(7-4)!}
= 35
total combinations = 11C3
= 11!/{3!(11-3)!}
P(all consonants) = 35/165
= 7/33
I understand all of the steps, except for why combinations is chosen rather than permutations. It is my understanding that combinations are used when the order of choices does not matter. However, in probability the order would matter - for example, the choice of SPL from the letters should be counted along with PSL, PLS, SLP etc.
When I calculated the example using permutations, I did not get 7/33:
consonant permutations = 7P3
= 7!/3!
= 840
total permutations = 11P3
=11!/3!
= 6 652 800
P(all consonants) = 840 / 6 652 800
= 1/7920
Can someone please explain my error in reasoning? I am very confused about why combinations is used instead of permutations.
Thank you!