Question:

A student has to answer $10$ questions, choosing atleast $4$ from each of parts $A$ and $B$. If there are $6$ questions in Part $A$ and $7$ in Part $B$, in how many ways can the student choose 10 questions ?

Updated On: Jul 6, 2022
  • $266$
  • $260$
  • $256$
  • $270$
Show Solution
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The Correct Option is A

Solution and Explanation

The possibilities are : $4$ from Part $A$ and $6$ from Part $B$ or $5$ from Part $A$ and $5$ from Part $B$ or $6$ from Part $A$ and $4$ from Part $B$. Therefore, the required number of ways $= \,^{6}C_{4} \times ^{7}C_{6} \times ^{6}C_{5} \times ^{7}C_{5} \times^{6}C_{6} \times ^{7}C_{4}$ $ = 105 + 126 + 35$ $=266$.
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Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.