A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
A. 392
B. 126
C. 26
D. 9
Answer: Option B
Solution(By Examveda Team)
There are 8 students and the maximum capacity of the cars together is 9. We may divide the 8 students as follows:Case I: 5 students in the first car and 3 in the second. Hence, 8 students are divided into groups of 5 and 3 in 8C3 = 56 ways.
Case II: 4 students in the first car and 4 in the second. So, 8 students are divided into two groups of 4 and 4 in 8C4 = 78 ways. Therefore, the total number of ways in which 8 students can travel is: 56 + 70 = 126
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Comments ( 1 )
Related Questions on Permutation and Combination
A. 3! 4! 8! 4!
B. 3! 8!
C. 4! 4!
D. 8! 4! 4!
A. 7560,60,1680
B. 7890,120,650
C. 7650,200,4444
D. None of these
A. 8 × 9!
B. 8 × 8!
C. 7 × 9!
D. 9 × 8!
8C5 + 8C4 = 58+70 = 126