Perm and Combination Problem

judisons2

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Joined
Mar 31, 2014
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5
:confused:Hi I have this perm and comb question where I don't really understand how to get the answer.
The question is:

How many four letter strings can be formed from the letters {a, b, c, d, e, f, g} if:
a) no repetition is allowed,
b) the strings must contain exactly two e’s,
c) the strings must contain at least two e’s.

so for b the answer was 216, I thought it would be 6x6 (because for the next 2 numbers you can select 6 choices each)
and c was 241. Can you please explain b & c to me.
 
this perm and comb question where I don't really understand how to get the answer.
The question is:
How many four letter strings can be formed from the letters {a, b, c, d, e, f, g} if:
a) no repetition is allowed,
b) the strings must contain exactly two e’s,
c) the strings must contain at least two e’s.
a) the answer is permutation of seven taken four: \(\displaystyle \mathbb{P}_4^7\).

b) From four places to choose two and place the two e's: \(\displaystyle \mathbb{C}_2^4\cdot\mathbb{P}_2^6\)

c) Find the number that contain no e or exactly one e and subtract from the total possible.
 
Hi

a) the answer is permutation of seven taken four: \(\displaystyle \mathbb{P}_4^7\).

b) From four places to choose two and place the two e's: \(\displaystyle \mathbb{C}_2^4\cdot\mathbb{P}_2^6\)

c) Find the number that contain no e or exactly one e and subtract from the total possible.


Thanks for your answers but your b does not give the solution indicated by the answers. :sad:
 
Thanks for your answers but your b does not give the solution indicated by the answers. :sad:
Assuming that this is about strings with no repetitions the answer I gave for b) is correct.

But otherwise it is \(\displaystyle \mathbb{C}^4_2\cdot 6^2\).
 
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