Question

In how many ways can 6 persons to be selected from 4 officers and 8 constables, if at least one officer is to be included

• A. 224
• B. 672
• C. 896
• D. None of these

Answer 1

Answer: (C)

896

Answer 2

Required number of ways =

$4C_{1} \times^{8}C_{5} +^{4} ⥂ C_{2} \times^{8} ⥂ C_{4} +^{4} ⥂ C_{3} \times^{8} ⥂ C_{3} +^{4} ⥂ C_{4} \times^{8} ⥂ C_{2}$

= 4 × 56 + 6 × 70 + 4 × 56 + 1 × 28 = 896.