Permutations & Combinations
Counting combinations with two types
MMTS_Full_Test_17
Grade 12
Question:
There are tea cups with and without handles. The number of ways of selecting 2 without handle and 3 with handle is exactly 1200. What is the maximum possible number of cups in the kitchen?
(A) 29
(B) 49
(C) 31
(D) 44
Step-by-Step Solution
Key Concept: $\binom{x}{2}\binom{y}{3}=1200$ where $x$ = cups without handle, $y$ = with handle. Find integer solutions.
Max $x+y=29$.
Correct Answer: (A) 29