How many distinct arrangements can be formed from all the letters of student In statics?

To find the number of distinct arrangements of the letters in "student," we first note that the Word contains 7 letters, with the letter 't' appearing twice. The formula for distinct arrangements of letters is given by ( \frac{n!}{p_1! \times p_2! \times \ldots \times p_k!} ), where ( n ) is the total number of letters and ( p_i ) are the frequencies of the repeated letters.

For "student," this results in:

[ \frac{7!}{2!} = \frac{5040}{2} = 2520. ]

Thus, there are 2,520 distinct arrangements of the letters in "student."