# From 4 Officers and 8 Jawans in How Many Ways Can 6 Be Chosen. to Include at Least One Officer? - Mathematics

From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?

#### Solution

From 4 officers and 8 jawans, 6 need to be chosen and at least one of them is an officer.
Required number of ways =  Total number of ways -  Number of ways in which no officer is selected

$=^{12} C_6 -^8 C_6$
$= \frac{12!}{6! 6!} - \frac{8!}{6! 2!}$
$= \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7}{6 \times 5 \times 4 \times 3 \times 2 \times 1} - \frac{8 \times 7}{2}$
$= 924 - 28$
$= 896$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 9.2 | Page 16