The answer is 50P3 = 50*49*48/(3*2*1) = 117,600
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The number of different ways you can arrange the letters MNOPQ is the number of permutations of 5 things taken 5 at a time. This is 5 factorial, or 120.
4! = 4*3*2*1 = 24 ways
you can arrange three beads 9 different ways.
Since the letter of the word COMPARE are distinct, i.e. none of them repeat, then the number of different way you can arrange them is simply the number of permutations of 7 things taken 7 at a time. That is 7! or 5040.
24.