Three letters are randomly selected from the 26 capital letters of the

1.	Three letters are randomly selected from the 26 capital letters of the English alphabet. What is the probability that letters A will not be included in the choice ?(a) \(\frac{1}{12}\)(b) \(\frac{23}{26}\)(c) \(\frac{12}{13}\)(d) \(\frac{25}{26}\)
Answer» (b) \(\frac{23}{26}\) Total number of ways in which 3 letters can be selected from 26 letters = ²⁶C₃. If A is not to be included in the choice, there are 25 letters left, so number of ways in which 3 letters can be selected without including A = ²⁵C₃. ∴ Required probability = \(\frac{^{25}C_3}{^{26}C_3}\) = \(\frac{25\times24\times23}{26\times25\times24}\) = \(\frac{23}{26}\).

Three letters are randomly selected from the 26 capital letters of the English alphabet. What is the probability that letters A will not be included in the choice ?(a) \(\frac{1}{12}\)(b) \(\frac{23}{26}\)(c) \(\frac{12}{13}\)(d) \(\frac{25}{26}\)

Answer»

(b) \(\frac{23}{26}\)

Total number of ways in which 3 letters can be selected from 26 letters

= ²⁶C₃.

If A is not to be included in the choice, there are 25 letters left, so number of ways in which 3 letters can be selected without including A

= ²⁵C₃.

∴ Required probability = \(\frac{^{25}C_3}{^{26}C_3}\) = \(\frac{25\times24\times23}{26\times25\times24}\) = \(\frac{23}{26}\).

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Three letters are randomly selected from the 26 capital letters of the English alphabet. What is the probability that letters A will not be included in the choice ?(a) \(\frac{1}{12}\)(b) \(\frac{23}{26}\)(c) \(\frac{12}{13}\)(d) \(\frac{25}{26}\)

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