There are 26 letters in the English alphabet. If we separate the group (a, some 5 letters, b), we will be left with 19 more letters. These 20 objects (1 group + 19 letters) can be arranged among themselves in 20! ways. Since either a or b can be at the beginning or the end of the group of 7 letters (a, some 5 letters, b), the number of possible arrangements of the group will be 2×(‌1P1×‌5P5×‌1P1)=2×5! Also, each group of 5 letters can be selected from the remaining 24 letters (except a and b) in 24C5 ways. Required total number of ways =(2×5!×‌24C5)×20! =2×‌24P5×20!