Question

Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. how many ways can the letters of emdangl be​ arranged? identify the correct​ unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.

Answer 1

The sequence "emdangl" rearranges to "mangled" (an appropriately fitting word scramble solution).

There are 7 letters in the sequence "emdangl", so there are 7! = 7*6*5*4*3*2*1 = 5040 different permutations of the seven letters. The exclamation mark is shorthand to represent factorial notation. Factorials are the idea of multiplying from that integer counting down until you get to 1. The reason why this works is because we have 7 letters to pick from for the first slot, then 6 for the next, and so on until all seven slots are filled out.

Since there is one solution ("mangled") out of 5040 total permutations, this means the probability of getting the solution just by random chance/guessing is 1/5040

Use a calculator shows that 1/5040 = 0.0001984 approximately.