With these question just write out the word but in terms of the occurrences of the letters.
1c,1h,1a,2l,2e,1n,1g
| Pattern | Select | Arrange | Total |
| x+y+z | 7c3 | 3! | 7c3x3! |
| 2x+y | 2c1x6c1 | 3!/(2!1!) | 2c1x6c1x3!/(2!1!) |
Summing the totals gives 246
Can you re-write the total of the first line using a different combinatoric notation? If so, why?
Note it would not be then valid to do a probability question, based on the number of outcomes listed above, since the outcomes arn't equally likely. For example: You would get 2 cases for the l's instead of 1 for the h etc.
You would need to regard the letters as distinguishable to produce equally likely outcomes, then you could evaluate the probability. To check here's a question. What's the probability that:
a) You select 3 vowels, one at a time
bi) You select 2 vowels and a consonant, simultaneously
bii) You select 2 vowels and a consonant one at a time
biii) You select 2 vowels and a consonant with repetition
