
Of all the 8 letter words that can be formed by using all letters of the word EQUATION. How many begin with the letter T?
(a) $8!$
(b) $\dfrac{7!}{2!}$
(c) $7!$
(d) $6!$
Answer
411.9k+ views
Hint: Form 8 boxes and fix the letter T in the first box. Now, fill the remaining 7 boxes with 7 letters that are remaining by using the formula that n number of different things can be arranged in $n!$ ways. Substitute n = 7 to get the answer.
Complete step by step answer:
Here we are provided with the word EQUATION and we are asked to find the number of 8 letters words that can be formed using the letters present in the word such that the first letter is always T.
Now, we can see that there are 8 different letters in the given word so let us form 8 boxes in which the letters can be filled. The first letter should be T as per the condition given in the question, so let us fill the first box with T. Therefore we have,
Now, we need to fill the remaining 7 boxes with 7 remaining letters of the word. We know that n things can be arranged in $n!$ ways if there are n positions. So we have,
$\Rightarrow $ Number of ways in which the remaining 7 letters of the given word can be arranged in 7 boxes = $7!$
So, the correct answer is “Option c”.
Note: Note that here none of the letters were repeating or appearing more than once. In case the letters appear more than once, we divide the total number of arrangements (considering all the letters different) with the product of factorial of number of times each letter is repeated. We use the formulas of permutations and combinations for the processes of arrangement and selection respectively.
Complete step by step answer:
Here we are provided with the word EQUATION and we are asked to find the number of 8 letters words that can be formed using the letters present in the word such that the first letter is always T.
Now, we can see that there are 8 different letters in the given word so let us form 8 boxes in which the letters can be filled. The first letter should be T as per the condition given in the question, so let us fill the first box with T. Therefore we have,
T |
Now, we need to fill the remaining 7 boxes with 7 remaining letters of the word. We know that n things can be arranged in $n!$ ways if there are n positions. So we have,
$\Rightarrow $ Number of ways in which the remaining 7 letters of the given word can be arranged in 7 boxes = $7!$
So, the correct answer is “Option c”.
Note: Note that here none of the letters were repeating or appearing more than once. In case the letters appear more than once, we divide the total number of arrangements (considering all the letters different) with the product of factorial of number of times each letter is repeated. We use the formulas of permutations and combinations for the processes of arrangement and selection respectively.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

The correct geometry and hybridization for XeF4 are class 11 chemistry CBSE

Water softening by Clarks process uses ACalcium bicarbonate class 11 chemistry CBSE

With reference to graphite and diamond which of the class 11 chemistry CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

How many valence electrons does nitrogen have class 11 chemistry CBSE
