JEE Maths›Permutations & Combinations›Visual Solution
Visual SolutionPYQ 2023 · Apr 10 Shift 2Standard
Question
Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is
(A)11201120
(B)33603360
(C)16801680
(D)560560
Solution Path
Only valid split is (3,3,2)(3, 3, 2). Ways =3×8C2×6C3=1680= 3 \times {}^{8}C_{2} \times {}^{6}C_{3} = 1680.
01Question Setup
1/4
8 persons in 3 distinct cars, each holding at most 3. Find the number of ways.
Ways=  ?\text{Ways} = \;?
02Find Valid Split
2/4
Only valid partition of 8 with max 3 per car: (3,3,2)(3, 3, 2). Choose which car gets 2: 33 ways.
(3,3,2)(3, 3, 2)
03Count WaysKEY INSIGHT
3/4
Choose 2 for smaller car: 8C2=28{}^{8}C_{2} = 28. Split remaining 6 into groups of 3: 6C3=20{}^{6}C_{3} = 20. Total: 3×28×20=16803 \times 28 \times 20 = 1680.
3×28×20=16803 \times 28 \times 20 = 1680
04Final Answer
4/4
Number of ways =1680= 1680.
1680\boxed{1680}
Want more practice?
Try more PYQs from this chapter →