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- Homework Statement
- Four letters are randomly selected from the word ENCYCLOPAEDIA. Find the probability that one letter E will occur in the selection of 4 letters.

- Relevant Equations
- [SUP]2[/SUP]C[SUB]1[/SUB] x [SUP]11[/SUP]C[SUB]3[/SUB]/[SUP]13[/SUP]C[SUB]4[/SUB] = 0.46

Four letters are randomly selected from the word ENCYCLOPAEDIA. Find the probability that one letter E will occur in the selection of 4 letters.

My calculation was

However, the answer is 2/33. I think the repeated letters might need to be accounted for. I divided the E term in the numerator by 2. I also divided the term for the remaining 11 letters by 4. I divided the denominator by 8 (2!x2!x2!), but this just canceled out the 2x4 in the numerator.

Thanks

My calculation was

^{2}C_{1}x^{11}C_{3}/^{13}C_{4}= 0.46However, the answer is 2/33. I think the repeated letters might need to be accounted for. I divided the E term in the numerator by 2. I also divided the term for the remaining 11 letters by 4. I divided the denominator by 8 (2!x2!x2!), but this just canceled out the 2x4 in the numerator.

Thanks

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