CAT 2000 — QA Question 8
Seating arrangementsEasy
One red flag, three white flags and two blue flags are arranged in a line such that,
(A) no two adjacent flags are of the same colour.
(B) the flags at the two ends of the line are of different colours.
In how many different ways can the flags be arranged?
Answer & solution
6
- B
4
- C
10
- D
2
Solution
First arrange one red and two blue flags in 3 ways. (i.e. BBR, BRB, RBB)
Now there are four positions (say 1, 2, 3, 4) to arrange 3 white flags. Since the flags at the ends are of different colours, two white flags can’t be at positions 1 and 4 simultaneously. Thus, the three flags can be arranged at 1, 2, 3 or 2, 3, 4 in 2 ways.
Thus, the six flags can be arranged in 3 × 2 = 6 ways.
Hence, option (a).