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Answer :
Final answer:
There are 1560 7-letter strings possible with 'a' before 'b' out of the given letters.
Explanation:
To find the number of 7-letter strings where 'a' must occur before 'b' out of the given letters (a, b, c, d, e, f, g), we can break it down into two cases:
- If 'a' is the first letter, then 'b' can be placed in any of the 6 remaining positions. The remaining 5 letters can be arranged in 5! ways. So, the total number of strings in this case is 6 x 5!
- If 'a' is not the first letter, then 'a' and 'b' can be placed in any of the 7 positions. The remaining 5 letters can be arranged in 5! ways. So, the total number of strings in this case is 7 x 5!
The total number of strings is the sum of the two cases: 6 x 5! + 7 x 5! = 720 + 840 = 1560.
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