Question

A club has 256 members, of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is ?

• A. 48
• B. 43
• C. 45
• D. 52
• E. 50

Answer 1

The Correct Option is B

Concept: Use inclusion-exclusion principle.
Step 1: Apply formula.} \[ \text{Total} = F + T + C - (FT + TC + FC) + (\text{all three}) \]
Step 2: Substitute values.} \[ 256 = 144 + 123 + 132 - (58 + 25 + 63) + x \]
Step 3: Solve for } x. \[ 256 = 399 - 146 + x \Rightarrow 256 = 253 + x \Rightarrow x = 3 \]
Step 4: Only tennis.} \[ \text{Only tennis} = T - (FT + TC) + (\text{all three}) \] \[ = 123 - (58 + 25) + 3 = 43 \]
Step 5: Final answer.} Thus, 43 members play only tennis.