What is the probability of forming the word "ADDS” by picking 4 ca

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What is the probability of forming the word "ADDS” by picking 4 cards at random and kept in the same order out of 50 cards given with 10 cards having "A”, 10 having "S” and the remaining 30 having "D” on it?

Options:

A .

\frac{2^{2}}{5^{4}}

B .

\frac{15}{(48 - 1) (48 + 1) \times 4}

C .

\frac{1}{50^{2}}

D . None of these

Answer: Option D
:
D

1) Probability of Getting an $A = \frac{10}{20} = \frac{1}{5}$
2) Probability of getting a $D = \frac{30}{49}$
3) Probability of getting a $D = \frac{29}{48}$
4) Probability of getting a $S = \frac{10}{47}$
Total probability= $\frac{1}{5} \times \frac{30}{49} \times \frac{29}{48} \times \frac{10}{47}$

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