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Class 11MathematicsPermutations and CombinationsCombinationsEasy
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In how many ways can a set of (3) questions be made from (10) different questions?

Answer and explanation

Correct answer: 120

Here, 3 questions are to be selected from 10 distinct questions, and the order of the selected questions does not matter. Therefore, use combinations: \(\binom{10}{3}=\frac{10!}{3!\,7!}=120\). Hence, 120 is the correct answer. A value such as \(720\) can result from counting arrangements as well, so it is not appropriate here. Exam tip: When a question asks for a selection or a set, usually use \(nCr\).

Related tags

CombinationsPermutations And CombinationsClass 11SelectionNcrMathematicsClass 11 Mcq
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10 more MCQs
  1. 1A shop has 6 different types of pencils and 2 different types of notebooks. In how many different ways can one pencil and one notebook be bought?
  2. 2A student chooses one subject from 3 subjects and one game from 5 games. How many different selections are possible in total?
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  4. 4An examination contains 6 short-answer questions and 4 long-answer questions. A student has to solve exactly one of them. In how many ways can the student choose the question?
  5. 5A meal plate offers 2 bread choices, 3 vegetable choices, and 2 dessert choices. In how many ways can a plate be prepared by choosing one item from each category?
  6. 6A bag contains pens in 3 different colors, markers in 4 different colors, and pencils in 2 different colors. In how many ways can one pen, one marker, and one pencil be chosen?
  7. 7A vehicle number consists of two letters followed by two digits. There are 4 choices for each letter and 10 choices for each digit. If repetition of letters and digits is allowed, how many distinct vehicle numbers can be formed?
  8. 8A bag has 6 red and 5 blue balls. Four balls are to be selected with equal numbers of both colours. How many selections are possible?
  9. 9If \(\frac{(n+2)!}{(n-2)!}=3024\), what is the value of \(n\)?
  10. 10What is the value of \(\frac{10!}{2!\cdot 8!}\times\frac{8}{9}\)?
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