Question

A box contains 10 balls out of which 3 are red and the rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?

• A. 105
• B. 168
• C. 189
• D. 120

Answer 1

The correct option is B 168

(B) The possible ways are as follows:
(i) 1 red ball out of the three and 5 blue balls out of the seven.
(ii) 2 red ball out of the three and 4 blue balls out of the seven.
$\therefore$ Total number of ways in which a random sample of six balls can be drawn
${=}^3{C}_1{\times }^7{C}_5{+}^3{C}_2{\times }^7{C}_4=169$