A team is made up of $11$ regulars and $9$ reserves. Selecting $4$ people from the team, how many distinct groupings can be formed?
2026-03-30 13:54:45.1774878885
A team is made up of $11$ regulars and $9$ reserves. Selecting $4$ people from the team, how many distinct groupings can be formed?
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I'm not sure I'm understanding the question completely, so let me explain my interpretation before giving an answer.
You have $11$ regular team members and $9$ reserve team members. We want to count the number of possible groups of 4 members that can be formed through any number of the regular or reserve team members.
In which case, imagine that all $20$ people are grouped together. We don't actually care whether they are regular or reserve team members, just pick $4$ from the total: $\binom{20}{4}$.