Fill in the Blank. ^ 15 C_8 + ^ 15 C_9 – ^ 15 C_6 – ^ 15 C_7 = _ … - Vidyadip

Question

Fill in the Blank.
$^{15}C_8 +\ ^{15}C_9\ –\ ^{15}C_6\ –\ ^{15}C_7 = \_\_\_\_\_\_.$

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Answer

$^{15}C_8 +\ ^{15}C_9 -\ ^{15}C_6 -\ ^{15}C_7 = 0$
Solution:
$^{15}\text{C}_8+\ ^{15}\text{C}_9-\ ^{15}\text{C}_6-\ ^{15}\text{C}_7=\ ^{15}\text{C}_8+\ ^{15}\text{C}_9-\ ^{15}\text{C}_{15-6}-\ ^{15}\text{C}_{15-7}$
$[\because\ ^\text{n}\text{C}_\text{r}=\ ^\text{n}\text{C}_\text{n-r}]$
$=\ ^{15}\text{C}_8+\ ^{15}\text{C}_9-\ ^{15}\text{C}_9-\ ^{15}\text{C}_8=0$

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