1. How many distinguishable letter arrangements can be made from the letters in the word STATISTICS?To find this you would find the number of letters in the word (10 in this case) and do factorial. You would divide this number by factorial of any letters that repeat. Since 'T' repeats 3 times, 'S' repeats 3 times, and 'I' repeats 2 times, you would divide the 10 factorial by (3 factorial times 3 factorial times 2 factorial)10! ÷ (3!*3!*2!) = 50400.I do not know how to solve the second problem though. I hope this helps.