There are 8 A-type, 2 B-Type and 4 C-type objects are in a bag. All the 14 objects are drawn one by

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20 Oct 2021 arrangement

There are 8 A-type, 2 B-Type and 4 C-type objects are in a bag. All the 14 objects are drawn one by one and arranged in a row. Find out the number of different arrangements possible.

OPtion

1. 40240
2. 50250
3. 50050
4. 55055
5. 62025
6. 66046
7. 45045
8. 48056
9. 42016
10. None of the above

Solution

Number of different arrangements possible = {14!} / {8! 2! 4!}
= {14×13×12×11×10×9×8×7×6×5×4×3×2 } / {(8×7×6×5×4×3×2 ) (2) (4×3×2)}}
= {14×13×12×11x10x9} / {(2)(4×3×2)} = {7×13×3×11x5×3} = 45045

Correct Option: 7 Best Solution (4)