## anonymous 3 years ago 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.

1. anonymous

Did u mean BCD togther?

2. kropot72

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: $4!\times 5$