How many distinct arrangements can be made from the word college? - Answers

The word "college" has 7 letters, including 2 'l's and 2 'g's, which are repeated. To find the number of distinct arrangements, we use the formula for permutations of multiset: [ \frac{n!}{n_1! \cdot n_2!} ] where (n) is the total number of letters, and (n_1), (n_2) are the frequencies of the repeated letters. Here, (n = 7), (n_1 = 2) (for 'l'), and (n_2 = 2) (for 'g'): [ \text{Distinct arrangements} = \frac{7!}{2! \cdot 2!} = \frac{5040}{4} = 1260. ] Thus, there are 1,260 distinct arrangements of the letters in "college."