Question:

Find the number of arrangements of the letters of the word when words begin with $I$ and end in $P$.

Updated On: Jul 6, 2022
  • $12400$
  • $12420$
  • $12620$
  • $12600$
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The Correct Option is D

Solution and Explanation

Let us fix $I$ and $P$ at the extreme ends ( $I$ at the left end and $P$ at the right end). We are left with $10$ letters. Hence, the required number of arrangements $= \frac{10!}{3! 2! 4!} = 12600$
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Notes on permutations and combinations

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.