A student is asked to answer 10 out of 13 questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is
A student is asked to answer 10 out of 13 questions in an examination such that he must answer at least four questions from the first five questions. Then the total number of possible choices available to him is
186
176
286
196
The Correct Option is D
Solution and Explanation
The correct option is (D) 196.
(i) Choosing 4 out of the first five questions and 6 out of the remaining 8 questions. Therefore, the number of choices in this case is given by 5C4×8C6=5C1×8C2=5×8×1×27=140.
(ii) Choosing 5 out of the first five questions and 5 out of the remaining 8 questions. This leads to 5C5×8C5=1×8C3=5×8×1×2×37=56.
Hence, the total number of choices is 140+56=196140+56=196.
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Concepts Used:
Combinations
The method of forming subsets by selecting data from a larger set in a way that the selection order does not matter is called the combination.
- It means 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.
- For example, Imagine you go to a restaurant and order some soup.
- Five toppings can complement the soup, namely:
- croutons,
- orange zest,
- grated cheese,
- chopped herbs,
- fried noodles.
But you are only allowed to pick three.
- There can be several ways in which you can enhance your soup with savory.
- The selection of three toppings (subset) from the five toppings (larger set) is called a combination.
Use of Combinations:
It is used for a group of data (where the order of data doesn’t matter).