Question

The first 7 alphabets are written down at random. What is the probability that the letters a,b,c irrespective of order always come together?

Answer 1

Answer:

Number of alphabets = 7 (a,b,c,d,e,f,g)

since a,b and c shall always come together irrespective of their order, they will be considered as a system.

Now, the effective number of alphabets = 5 [(abc),d,e,f,g]

Number of ways of arranging these 5 alphabets = 5! = 1×2×3×4×5 = 120

Since, the alphabets a,b,c can be interchanged while still always being together. Number of ways of this arrangements = 3! = 1×2×3 = 6

Thus, the probability that the letters a,b,c irrespective of order always come together = 5! ×3! = 120×6 = 720

Answer 2

Step-by-step explanation:

The first 7 alphabets are written down at random. What is the probability that the letters a,b,c irrespective of order always come together?