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JP Morgan·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Quant engineer interview at JP Morgan with a probability/combinatorics problem. Pretty focused on the math, no fluff.

Questions Asked (1)

Q1

You have 5 male-female couples (10 people total). If you pick 4 at random, what's the probability that exactly 2 complete couples are chosen?

Algorithms & Data Structures
Author's notes

Took me a minute to set up the counting correctly.

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AI HintsAI Generated

Suggested Approach

Use combinatorics to count the total number of ways to choose 4 people from 10, then count the favorable outcomes where exactly 2 complete couples are selected. The favorable count involves choosing 2 couples out of 5 and then selecting 2 individuals from the remaining 3 couples such that they do not form a complete couple.

Pro tip: Clearly explain your reasoning step-by-step, as interviewers value logical clarity over just the final answer. Double-check that your favorable count excludes any possibility of a third complete couple.

1. Calculate total outcomes

Compute the total number of ways to choose 4 people from 10 using combinations: C(10,4).

2. Choose the complete couples

Determine the number of ways to choose exactly 2 complete couples from the 5 available: C(5,2).

3. Choose the remaining individuals

From the remaining 3 couples (6 people), choose 2 individuals such that they do not form a complete couple. This can be done by subtracting the number of ways to choose a complete couple from the total ways to choose 2 from 6: C(6,2) - C(3,1).

4. Compute favorable outcomes

Multiply the results from steps 2 and 3 to get the total number of favorable outcomes.

5. Calculate probability

Divide the favorable outcomes by the total outcomes to get the probability.

Key Points to Mention

  • Use of combinations (nCr) to count selections without order.
  • The total number of ways to choose 4 from 10 is 210.
  • There are 10 ways to choose 2 complete couples from 5.
  • From the remaining 3 couples, there are 12 ways to choose 2 people who are not a complete couple (15 total pairs minus 3 complete couples).
  • The favorable outcomes are 10 * 12 = 120.
  • The probability simplifies to 4/7.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.