self Maths Puzzle

In the word RAINBOW how many words are there in which A is always before I and I is always before O?
a)840
b)420
c)720
d)none of these

please explain the method clearly

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self Other Question

6.25:1.5811::??:1.8708

Find it? With explanation.
What is the relationship between the 3 sequences given by:
S1: 1,5,14,30... S2: 5,17,35,59...
S3: 1,17,98,354...