CAT 2004 — QA Question 29
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?
Answer & solution
- A
15
56
- C
120
- D
336
To reach point B from A, the car has to take a northward route thrice and a westward route five times. Thus we can visualise a set of 8 routes out of which 3 will be northward and 5 westward.
The number of ways in which the car can reach point B from A is a permutation of 8 routes, 5 (W) and 3 (N) of which are repeated.
Thus, number of ways = = 56
Hence, option (b).