Need help with two Permutation & Combinatorics questions

[MoniqueK]

(1) In how many ways can the letters of the word 'SIMLA' be rearranged, such that the vowels are never together?


(2) In how many ways can 5 boys and 6 girls be arranged in a rose, such that no two boys are together?

[earth@work]

is the OA:
1)3*4! =72
let vowels I & A be together = 4P4*2=4! *2
total arrangements=5!
never together arrangements = 5!-2*4! =4!*3 = 72
2)6!*5!
Girls:6 boys:7; arrangements are:
G1B1G2B2G3B3G4B4G5B5G6 or G1G2B1G3B2G4B3G5B4G6B5 etc but the arrangement will be equal to 5!*6!