Find the number of four letter arrangements of the letters of the word shoot
Formula Used: \[{}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}{\rm{ }},{\rm{ }}{}^n{P_r} = \dfrac{{n!}}{{\left( {n - r} \right)!}}\] Show Complete step-by-step answer: (i)Part No 1st (ii)Part No 2nd (iii)Part No 3rd (iv)Part No 4th (v)Part No 5th (vi)Part No 6th (vii)Part No 7th (viii)Part No 8th Note: We should always take care of where we should use permutation and where combination both seems confusing but have defined work. Combinations are used for groups here order doesn’t matter and Permutations are used for creating multiple lists. How many arrangements for a 4 letter word?4*6*5*4=480. Add 'em up: 1020 total arrangements.
How many fourHence, The total number of four-letter words that can be formed is 270. Therefore, option D. is the correct answer.
How many permutations are there in 4 letters?∴ Total number of ways in which 4 letter words are formed =1680+378+18+378=2454 ways.
|