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Permutation and Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSPermutation and Combinations1 Mark
Question
Fill in the Blank.
15C8 + 15C9 – 15C6 – 15C7 = ______.
✓

Answer

15C8 + 15C9 – 15C6 – 15C7 = 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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