Question

How many permutations of the letters ABCDEFG contain:
a.) the string BCD?
b.) the string CFGA?
c.) the strings BA and GF?

if you can explain, that would be awesome! Thank you kindly.

Answer 1

Did u mean BCD togther?

Answer 2

a.) Assuming "the string BCD" means the three letters are grouped together, the number of permutations of the 7 letters containing the string BCD will equal the possible number of permutations of the remaining 4 letters.
Each permutation of AEFG can be placed in 5 possible ways relative to the string as follows:
1. 0 letters before the string
2. 1 letter before the string
3. 2 letters before the string
4. 3 letters before the string
5. 4 letters before the string
Therefore the required number of permutations is:
\[4!\times 5\]