# There Are 13 Players of Cricket, Out of Which 4 Are Bowlers. in How Many Ways a Team of Eleven Be Selected from Them So as to Include at Least Two Bowlers? (A) 72 (B) 78 (C) 42 (D) None of These - Mathematics

MCQ

There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?

#### Options

• 72

• 78

•  42

• none of these

#### Solution

78
4 out of 13 players are bowlers.
In other words, 9 players are not bowlers.
A team of 11 is to be selected so as to include at least 2 bowlers.

$\therefore \text{Number of ways} =^4 C_2 \times^9 C_9 + {}^4 C_3 \times^9 C_8 + {}^4 C_4 \times^9 C_7$
$= 6 + 36 + 36$
$= 78$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 16 | Page 26