A navy admiral , has to choose 3 ships out of his fleet of 8 destroyer ships .…
2024
A navy admiral , has to choose 3 ships out of his fleet of 8 destroyer ships . In how many ways can this be achieved , assuming that he is not biased toward choosing any particular ship ?
- A.
120
- B.
48
- C.
56
- D.
336
Attempted by 38 students.
Show answer & explanation
Correct answer: C
Answer: 56
Key idea: Selecting 3 ships from 8 is a combination problem because the order of selection does not matter.
Use the combination formula nCr = n! / (r! (n−r)!).
Substitute n = 8 and r = 3: 8C3 = 8! / (3!·5!).
Compute: (8×7×6) / (3×2×1) = 336 / 6 = 56.
Note: If order mattered, you would use permutations: 8P3 = 8×7×6 = 336. Because order does not matter here, divide by 3! to get 56.