Bea has written a computer program that randomly generates 7 letters of the alphabet without replacement, what is the chance a random list will contain her name, such as, 'cbeadfk'. Answer as a fully simplified fraction.
My solution is: There are 26 letters in the alphabet and 7 are chosen each time, therefore the number of possible permutations is, 26P7 = 3315312000. We are interested in strings containing B, E, A in that order so we take those letters out of the alphabet and string, leaving 4 positions with 23 letters to choose from. The string bea can appear in 5 different permutations for each arrangement of the remaining 4 letters. So the amount of strings containing bea is (23P4)*5 = 1062600 favourable/total = 1062600/3315312000=1/3120
Is my answer correct?