Hi - I'm having difficulty in visualizing problems of the types where 3 or more elements do NOT have to be together in permutation problems:
Problem 1: How many ways can the letters of RAINBOW be arranged so that the vowels are never together?
or
Problems 2: How many ways can 6 students and 4 teachers be seated so that no 2 teachers are together?
Now, the answer explanation says that:
Problem 1 - 4 consonant can be arranged in 4! ways which leaves us with 5 places to place the 3 vowels - HOW 5 PLACES?? IT SHOULD BE 3 PLACES, RIGHT?
Problem 2- 6 students can sit in 6! ways, which leaves 7 places to seat the 4 teachers - AGAIN, HOW 7 PLACES??
Please help.
Tanvi
Problem 1: How many ways can the letters of RAINBOW be arranged so that the vowels are never together?
or
Problems 2: How many ways can 6 students and 4 teachers be seated so that no 2 teachers are together?
Now, the answer explanation says that:
Problem 1 - 4 consonant can be arranged in 4! ways which leaves us with 5 places to place the 3 vowels - HOW 5 PLACES?? IT SHOULD BE 3 PLACES, RIGHT?
Problem 2- 6 students can sit in 6! ways, which leaves 7 places to seat the 4 teachers - AGAIN, HOW 7 PLACES??
Please help.
Tanvi
