A box I contain letters of 3 white, 1 blue and 2 yellow color another

1.	A box I contain letters of 3 white, 1 blue and 2 yellow color another box II contain letters of 5 white, 3 blue and 4 yellow color, if all the letters are mixed in box III and 2 letters are picked without replacing, then what is the possibility that the letters are not white?1. \(7\over 17\)2. \(4\over 9\)3. \(10\over 17\)4. \(5\over 17\)
Answer» Correct Answer - Option 4 : \(5\over 17\) Concept: General Rule: The number of ways for selecting r from a group of n (n > r) = nCr The probability of particular case = \(\rm \text{Number of ways for the case can be executed}\over{\text{Total number of ways for selection}}\) Calculation: The total letters in box III = 3 + 1 + 2 + 5 + 3 + 4 = 18 Out of which: White letters = 3 + 5 = 8 Blue letters = 1 + 3 = 4 Yellow letters = 2 + 4 = 6 Ways of selecting 2 letters out of 18 without replacement = ¹⁸C₂ Ways of selecting 2 letters out of 10 not white letters without replacement = 10C2 Possibility of the letters picked are not white = \(\rm ^{10}C_2\over^{18}C_2\) = \(5\over 17\)

A box I contain letters of 3 white, 1 blue and 2 yellow color another box II contain letters of 5 white, 3 blue and 4 yellow color, if all the letters are mixed in box III and 2 letters are picked without replacing, then what is the possibility that the letters are not white?1. \(7\over 17\)2. \(4\over 9\)3. \(10\over 17\)4. \(5\over 17\)

Answer» Correct Answer - Option 4 : \(5\over 17\)

Concept:

General Rule:

The number of ways for selecting r from a group of n (n > r) = nCr
The probability of particular case = \(\rm \text{Number of ways for the case can be executed}\over{\text{Total number of ways for selection}}\)

Calculation:

The total letters in box III = 3 + 1 + 2 + 5 + 3 + 4 = 18

Out of which:

White letters = 3 + 5 = 8

Blue letters = 1 + 3 = 4

Yellow letters = 2 + 4 = 6

Ways of selecting 2 letters out of 18 without replacement = ¹⁸C₂

Ways of selecting 2 letters out of 10 not white letters without replacement = 10C2

Possibility of the letters picked are not white = \(\rm ^{10}C_2\over^{18}C_2\) = \(5\over 17\)