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Your first question needs to be divided by 3! because order of group does not count. Hence, answer should be 6c2*4c2/3!
Second question is 5! - 4! = 120 - 24 = 96
4! is total number of unfavorable outcomes when 2 Gs(as a single entity) are next to each other:
(GG) - D - E - F --> 4! ways of sorting these differently
I am wrong for the second question:
Total outcome should be 5!/2! because there are 2 G's which can be interchanged. --> 60
4! would be all unfavorable outcomes as previously explained
Answer should be: 60 - 24 = 36
how mnay words can you make where the two G's are not together!
Do the words have to be real words ? Or just any combination of letters as long as the two Gs are not together.
If the words have to be real:
Then the number of words = 0 (The only word that can be made is egg, and it's out because the two g's are together)
If it's any letters and the words do not need to make sense:
Then , we can either has 1 letter word, 2 letter words, 3 letter words, 4 letter words, can't be 5 as that will give 2 g's
So 1 letter word - 5
2 letter words - 4P2 (remove 1 G) = 12 (use permutation assuming we can swtich the letters around and form another word)
3 letter words - 4P3 = 24
4 letter words - 4P4 = 16
ywilfred, I believe that you have to use all the letters to form a 5 letter word. Also, why did you omit to account for 5 letter words in your calculation? Although there are 2 G's, you should still account for words that can be formed when the 2 G's are apart.