MathematicsA box contains two white, three black and four red balls. The number of ways in which we can select three balls from the box, if at least one black ball is to be included in the selection, is

A box contains two white, three black and four red balls. The number of ways in which we can select three balls from the box, if at least one black ball is to be included in the selection, is

A
$2^{6}$
B
$2^{5}$
C
$2^{7} - 2^{6}$
D
none of these

Solution:

$∴$ Number of ways $=^{3} C_{1} \times^{6} C_{2} +^{3} C_{2} \times^{6} C_{1} +^{3} C_{3} \times^{6} C_{0}$

$= 64 = 2^{6}$

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