How many arrangements of the word EQUATION begins and ends with a consonant
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In the word "EQUATION" there are 3 consonants (Q,T,N) so there are $3!$ ways to arrange and 5 vowels (E,U,A,I,O) so $5!$ ways to arrange. In whole for both first consonant and then vowels or vice-versa, there are $2!$ ways . so in total $2! \cdot 5! \cdot 3!=1440$ ways. Show 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#. How many arrangements are there of the word EQUATION?Therefore, 1440 words with or without meaning, can be formed using all the letters of the word 'EQUATION', at a time so that the vowels and consonants occur together.
How many consonants are in a word?There are 24 consonant sounds in most English accents, conveyed by 21 letters of the regular English alphabet (sometimes in combination, e.g., ch and th).
How many 5 letter words can be formed from the word EQUATION?We know that nPr=n! (n−r)! Therefore , 15120 five letter words can be forms with the letters of the word EQUATIONS without repetition.
How many words of 4 letters beginning with A or E can be formed with the letters of the word equator '?Hence, The total number of four-letter words that can be formed is 270. Therefore, option D. is the correct answer.
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