Explanation
Solution
Concept:
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Combinations: Number of ways to select r distinct objects from n objects is nCr=r!(n−r)!n!.
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Permutations: Number of ways to arrange r objects in n places is nPr=(n−r)!n!.
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Relationship: nPr=nCr×r!.
Calculation:
There are 26 letters in total. If we separate a group containing (a, 5 letters, b), we are left with 26−7=19 more letters.
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Arrange the Group: The group (1 group+19 letters) contains 20 objects, which can be arranged in 20! ways.
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Internal Arrangement: In the group of 7 letters, a and b can swap positions (at the start or end), which gives 2 ways.
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Selection and Arrangement of 5 letters: We must select 5 letters from the remaining 24 letters (excluding a and b) and arrange them between a and b. This is done in 24P5 ways.
Total number of ways:
Correct Option: 3
