What are the number of different words beginning and ending with a consonant, which can made out of the word "EQUATION" ? (Using the concept of Permutations-Combinations)

Answer 1

4320 ways

The word "Equation" has 8 letters all of which are unique.

We want the number of letter arrangements that start and end with a consonant. Let's first see that with letter arrangements, we're working with permutations (we care about the order of things). The general formula is:

#P_(n,k)=(n!)/((n-k)!); n="population", k="picks"#

First let's work with the end letters. We only want consonants (there are 3 of them), which gives:

#P_(3,2)=(3!)/(1!)=6#
For the letters in between the end letters, there are 6 of them (5 vowels and the one consonant we didn't use) and can be placed anywhere. That's #6! = 720#.

In total then, we have

#6xx720=4320#
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Answer 2

There are 120 different words beginning and ending with a consonant that can be made out of the word "EQUATION".

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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