GATE 2026 XH2 (English) – Question 25
A police station has six personnel comprising an inspector (I) and five constables ($C_1, C_2, C_3, C_4, C_5$). Normally, a ‘raid team’ of two, three, or four members is formed depending upon the nature of the raid. As per rule, it is mandatory that the inspector is part of raid team.
Number of distinct raid teams that can be formed is __________________. (Answer in integer)
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Correct answer: 25
Explanation
The inspector is always in the team, so choose the other members from the five constables. A team of 2 needs 1 constable ($\binom{5}{1} = 5$ ways), a team of 3 needs 2 ($\binom{5}{2} = 10$ ways) and a team of 4 needs 3 ($\binom{5}{3} = 10$ ways). The total is $5 + 10 + 10 = 25$.