Q58 / 160 · TS EAMCET 2024 (10 May Shift 1) · Mathematics

A question paper has 3 parts $A, B, C$. Part $A$ contains 7 questions, part $B$ contains 5 questions and Part $C$ contains 3 questions. If a candidate is allowed to answer not more than 4 questions from part $A$; not more than 3 questions from part $B$ and not more than 2 questions from part $C$, then the number of ways in which a candidate can answer exactly 7 questions is

  • Correct answer
    A
    4655
  • B
    4025
  • C
    3675
  • D
    2625

Solution

A question paper has 3 parts $A, B, C$ $A B C$ $\downarrow \downarrow \downarrow$ $7 \quad 5 \quad 3 \leftarrow$ No. of Question Student can take maximum 4 questions, 3 questions and 2 questions from part $A, B$ and $C$ respectively. The number of ways student answer exactly 7 questions $\begin{array}{cccccc}=7 C_4 \times 5 C_3+7 C_4 \times 5 C_2 \times 3 C_1 \\ \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\ A & B & A & B & \stackrel{4}{C}\end{array}$ $=350+1050+1050+2205=4655$.

Hence, the correct answer is option: 'A'.

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