Here is an incorrect solution to a problem. Find the error, explain why it is no

Question

Here is an incorrect solution to a problem. Find the error, explain why it is not correct, and give the correct answer.

Here is an incorrect solution to a problem. Find the error, explain why it is not correct, and give the correct answer. "Problem: Find the number of ways to get two pairs of two different ranks {such as 2 jacks and 2 fives) in a 4-card hand from an ordinary deck of 52 card s." "Solution: There are 13 ways to get a rank {such as "kings") for the first pair and (4/2) ways to get a pair of that rank. Similarly, there are 12 ways to get a rank {such as "sevens") for the second pair and (4/2) ways to get a pair of that rank. Therefore there are ways to get 2 pairs."

Explanation / Answer

The error is that if we pick pairs from we are not choosing the ranks rather we are taking 13X12 possible cases, but in reality there can be (2 twos and 2 threes) and (2 threes and 2 twos) which are counted twice in the given solution.

The correct answer would be = 13C2X4C2X4C2 = 13*12*4*3*4*3/(2*2*2) = 2808

But in the given solution, it is 2*2808 = 5616 which is double the actual count

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.