In tossing two unbiased dice, success is defined as an outcome of a doublet. If $\frac{5^a}{2^b3^c}$ is the probability of first success occurs at 5th throw of a pair of dice, then a + 2b + 3c is equal to:

29

Since success comes at 5^th row.

∴ P(F₁F₂F₃F₄S₅) = P(F₁).P(F₂).P(F₃).P(F₄).P(S₅)

$=(\frac{30}{36})(\frac{30}{36})(\frac{30}{36})(\frac{30}{36})(\frac{6}{36})$

$=(\frac{5}{6})(\frac{5}{6})(\frac{5}{6})(\frac{5}{6})(\frac{1}{6})$

$⇒\frac{5^a}{2^b3^c}=\frac{5^4}{6^5}=\frac{5^4}{2^53^5}$

⇒ a = 4, b = 5, c = 5

∴ a + 2b + 3c = 4 + 2(5) + 3(5) = 4 + 10 + 15 = 29