The students can be selected in 10626 ways to be elected as President, Vice President, and Treasurer out of the 23 students, using permutation 23P3, since the order of selection matters.
What is Permutation?
The act of organizing all the components of a set into some sequence or order is known as permutation. Permuting, in other words, is the act of reordering the components of a set that has previously been sorted.
A permutation is the selection of r items from a collection of n items without replacement, with the order of the items being significant.
nPr = (n!) / (n-r)!
What is a Combination?
The combination is a method of picking elements from a collection in which the order of selection is irrelevant (unlike permutations).
A combination is a selection of r items from a collection of n items with no replacements and no regard for order.
nCr = (n!)/{(r!)((n-r)!)}
How do we solve the given question?
In the question, we are given that there are 23 students in a homeroom.
We are asked in how many ways can they be chosen to be elected President, Vice President, and Treasurer.
Since, the order of selection matters, in this case, we will use Permutation.
Hence, the number of ways in which the students can be chosen = 23P3.
To calculate this, we use the formula for permutation: nPr = (n!) / (n-r)!
∴ 23P3 = 23!/(23-3)!
or, 23P3 = 23!/20! = (20!*21*22*23)/20! = 21*22*23 = 10626.
∴ The students can be selected in 10626 ways to be elected as President, Vice President, and Treasurer out of the 23 students, using permutation 23P3, since the order of selection matters.
Learn more about Permutation and Combination at
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