Question

# How many meaningful English words can be formed with the letters ESRO using each letter only once in each word?A). NoneB). OneC). TwoD). Three

In this question, we have given ‘a’ word ESRO. It has 4 letters namely E, S, R, O. If we have to just rearrange letters then we can use permutation formula to get this, ${}^n{P_r} = \dfrac{{n!}}{{(n - r)!}}$. Since we are taking four out of four so ‘n’ and ‘r’ both will be equal to 4.
${}^4{P_4} = \dfrac{{4!}}{{(4 - 4)!}} = \dfrac{{4!}}{{0!}} = 4! = 24$
Note: Many students get confused when to use permutation and when to use the combination. A combination is always used to choose the items. For example, if we have n items and we have to choose ‘r’ out of that then we’ll use the combination. Its formula is ${}^n{C_r} = \dfrac{{n!}}{{r!(n - r)!}}$. On the other hand, the permutation is used for arrangements.