There are four routes to travel from city A to city B and six routes from city B to city C. How many routes are possible to travel from the city A to city C?

Correct Option (1)

The problem involves determining the total number of possible routes for a journey comprising sequential stages. The fundamental principle applicable here is the multiplication principle of counting. This principle states that if an event can occur in 'm' distinct ways, and following this, another independent event can occur in 'n' distinct ways, then the total number of ways both events can occur in sequence is m × n.

• Number of routes from city A to city B = 4.
• Number of routes from city B to city C = 6.

Applying the multiplication principle, the total number of possible routes from city A to city C is 4 × 6 = 24.

Incorrect Options:

Options 2, 3, and 4 are incorrect as they do not apply the appropriate combinatorial principle for sequential events.

• Option 3 (10) results from the addition of the number of routes (4 + 6). The addition principle is used when selecting one item from mutually exclusive sets, not for combining choices that occur in a sequence.
• Options 2 (12) and 4 (8) do not correspond to any valid combinatorial calculation for the given problem structure involving sequential route selection.