If $^{16} C_{r} =$ $^{16} C_{r + 2}$ , then find $^{r} C_{4}$ .

35

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45

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20

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40

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Solution

The correct option is A $35$
$^{16} C_{r} =^{16} C_{r + 2}$

Use the formula: $^{n} C_{x} =^{n} C_{y} \Rightarrow x + y = n$

$r + r + 2 = 16$

$2 r + 2 = 16$

$r = 7$

$^{r} C_{4} =^{7} C_{4} = \frac{7!}{4! 3!} = \frac{7 \cdot 6 \cdot 5}{3 \cdot 2 \cdot 1} = 35$

Thus, the value is 35.

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If $^{16} C_{2 r} =^{16} C_{r + 2^{'}}$ find $^{r} C_{4}$

16 \sum r = 2^{16} C_{r} =

30 - 35, 35 - 40

40 - 45

Age	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
Number of persons	$170$	$110$	$80$	$45$	$40$	$35$

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