From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is
A
less than 500
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
at least 500 but less than 750
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
at least 750 but less than 1000
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
at least 1000
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is B at least 1000 Let N1N2N3…N6 be novels and D1D2D3 be dictionaries The number of ways =6C4×3C1×(4!)
NNDNN Here, 6C4 denotes the selection of 4 novels out of 6,3C1 denotes the selection of 1 dictionary out of 3 and (4!) denotes the rearrangement of 4 novels as dictionary will always be in the middle. =15×3×24=1080 Hence, option 'D' is correct.