Tardigrade - CET NEET JEE Exam App
© 2022 Tardigrade®. All rights reserved Answer Hint: Here we calculate the number of letters in the given word. We calculate ways to fill each position using the concept of combination where we reduce the number of letters available for the next position by one after filling each position.* Combination is given by \[^n{C_r} = \dfrac{{n!}}{{(n - r)!r!}}\], where n is the total number of available objects and r is the number of objects we have to choose. * Factorial terms open up as \[n! = n(n - 1)!\] Complete step-by-step answer: Note: Alternative method: Number of ways to fill each position is given by \[n!\]where n is the number of letters available.So, number of 8 letter words formed is given by \[8!\]Use the expansion of factorial i.e. \[n! = n.(n - 1).(n - 2)......3.2.1\]\[ \Rightarrow 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\]\[ \Rightarrow 8! = 40,320\]So, total number of words formed is 40,320Now we have to find the words that start with T and end with E.So we fix the letters for the first and the eighth position and find a number of ways to fill all the remaining positions.So, number of ways to fill first position is 1 (only T)Number of ways to fill eighth position is 1(only E)Now to fill 6 positions we have 6 letters.Number of words formed is \[1 \times 6! \times 1\]Use the expansion of factorial i.e. \[n! = n.(n - 1).(n - 2)......3.2.1\]\[ \Rightarrow 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1\]\[ \Rightarrow 6! = 720\]So, the number of words formed is 720. |