Question

The results of 21 football matches (win, lose,draw) are to be predicted. The no. of different forecasts that can contain 19 wins is

• A. $210$
• B. $640$
• C. $840$
• D. $1260$

Answer 1

The correct option is C $840$

Out of 21 matches 19 matches were won,
So there will be three cases:
case1) 19 win, 2 lose
Number of ways $=\frac{21!}{19!\times 2!}=210$
case2) 19 win, 1 lose, 1 draw
Number of ways $=\frac{21!}{19!}=420$
case3) 19 win, 2 draw
Number of ways $=\frac{21!}{19!\times 2!}=210$
$\therefore$ total number of ways $=210+420+210=840$