COMEDK · Maths · 4. Permutation Combination
A coach needs to select a 4 - player starting lineup from a pool of 10 players:
5 guards
3 forwards
2 centres
Find the number of different selections if the 4-player starting lineup must include:
At least 1 guard
At most 1 forward
Exactly 1 centre
- A \(60\)
- B \(80\)
- C \(70\)
- D \(20\)
Answer & Solution
Correct Answer
(B) \(80\)
Step-by-step Solution
Detailed explanation
Let \(g\), \(f\), and \(c\) be the number of guards, forwards, and centres selected respectively. We are given the following conditions: \(g + f + c = 4\) \(g \ge 1\) \(f \le 1\) \(c = 1\) Substituting \(c = 1\) into the first equation, we get \(g + f = 3\). Since \(f \le 1\),…
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