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lg800
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M05-17 03 May 2023, 17:29
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Why do you use a combination instead of a permutation? Doesn't the order matter if its HTTTT vs HTTTT?
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Bunuel
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M05-17 04 May 2023, 00:13
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lg800
Why do you use a combination instead of a permutation? Doesn't the order matter if its HTTTT vs HTTTT?
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Yes, the order matters. For example, HTTTT (first is heads, then four tails) case is different from TTTTH (first four tails, then heads) case. Hence we need all permutations of four heads and one tail. I suggest you to study the following links:


21. Combinatorics/Counting Methods



For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread


Hope it helps.
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M05-17 21 Nov 2023, 12:23
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I think this is a high-quality question and I agree with explanation.
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M05-17 03 Apr 2024, 20:26
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Bunuel
Kate and David each start with $10. They flip a coin 5 times. For each flip that results in heads, Kate gives David $1, and for each flip that results in tails, David gives Kate $1. After flipping the coin 5 times, what is the probability that Kate has more than $10 but less than $15?

A. \(\frac{5}{16}\)
B. \(\frac{15}{32}\)
C. \(\frac{1}{2}\)
D. \(\frac{21}{32}\)
E. \(\frac{11}{16}\)
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­10$ < Kate < 15$

If she wins 2 times then Kate will have : 12-3 = 9$
If Kate wins 1 time then , Kate will have : 11-4 = 7$
If she wins 5 times then , Kate will have 15$

So, Kate can get between 10$ to 15$ , if she wins 3 out of 5 times or 4 out of 5 times. 

Probability of getting Head =\( \frac{ 1 }{ (2^5) } = \frac{ 1}{32 } \)

Probability of getting 3 Heads out of 5 flips =
      \( 5 C 3 \) * (\( \frac{ 1 }{ 32 } \) ) = \( \frac{ 10 }{ 32 } \) 

Probability of getting 4 Heads out of 5 flips =  
     \( 5 C 4 \) * ( \( \frac{ 1 }{ 32 } \)) = \( \frac{ 5 }{ 32 } \) 

Combined =\( \frac{ 15}{32 }\)­
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M05-17 01 Dec 2024, 07:52
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I think this is a high-quality question and I agree with the explanation.
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M05-17 13 Jan 2025, 23:16
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I like the solution - it’s helpful.
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M05-17 03 Sep 2025, 00:04
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I like the solution - it’s helpful.
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M05-17 06 Sep 2025, 10:08
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I like the solution - it’s helpful.
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M05-17 26 Oct 2025, 12:05
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I don’t quite agree with the solution. Although the prob of TTTHH and TTHHH are the same, in both cases, Kate will have more than $10 and less than $15. In that case, isn’t it right to include both the cases? Same with TTTTH and THHHH. Kate needs a minimum of $11 and a maximum of $14. That can happen in THHHH, TTHHH, TTTHH & TTTTH. Hence I got 15/16 as my final answer, however i guessed the approach mentioned in the answer might have been taken and answered 15/32. Please clarify.
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M05-17 26 Oct 2025, 12:09
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Aritrakarak
I don’t quite agree with the solution. Although the prob of TTTHH and TTHHH are the same, in both cases, Kate will have more than $10 and less than $15. In that case, isn’t it right to include both the cases? Same with TTTTH and THHHH. Kate needs a minimum of $11 and a maximum of $14. That can happen in THHHH, TTHHH, TTTHH & TTTTH. Hence I got 15/16 as my final answer, however i guessed the approach mentioned in the answer might have been taken and answered 15/32. Please clarify.
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You reversed wins and losses. Heads means Kate gives $1, tails means she gets $1. So she gains only when tails occur. To end with more than $10 but less than $15, she needs 3 or 4 tails, not 1 or 2. Hence the probability is 15/32, not 15/16. Please review the question and the solution more carefully.
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M05-17 04 Jan 2026, 06:11
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I like the solution - it’s helpful.
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