The number of divisors of the number ( displaystyle∑ r =120 5 r -1 19 C r -1/ displaystyle∑ r =017 17 C r 417- r 2 r ) is equal to

Question

The number of divisors of the number ( displaystyle∑ r =120 5 r -1 19 C r -1/ displaystyle∑ r =017 17 C r 417- r 2 r ) is equal to (A) 4 (B) 6 (C) 9 (D) 18

Tardigrade Admin · Accepted Answer

( displaystyle∑ r =120 5 r -1 19 C r -1/ displaystyle∑ r =017 17 C r 417- r 2 r )=( displaystyle∑ r =120 5 r -1 ⋅ 120- r ⋅ 19 C r -1/ displaystyle∑ r =017 17 C r 417- r 2 r )=(619/617)=36 Total number of factor of 36 is 9

Q. The number of divisors of the number $\frac{r = 1 \sum 20 5 ^{r - 1} ^{19} C _{r - 1}}{r = 0 \sum 17 ^{17} C _{r} 4 ^{17 - r} 2 ^{r}}$ is equal to

4

6

9

18

$\frac{r = 1 \sum 20 5 ^{r - 1} ^{19} C _{r - 1}}{r = 0 \sum 17 ^{17} C _{r} 4 ^{17 - r} 2 ^{r}} = \frac{r = 1 \sum 20 5 ^{r - 1} \cdot 1 ^{20 - r} \cdot ^{19} C _{r - 1}}{r = 0 \sum 17 ^{17} C _{r} 4 ^{17 - r} 2 ^{r}} = \frac{6 ^{19}}{6 ^{17}} = 36$
Total number of factor of 36 is 9

Q. The number of divisors of the number r=0∑17​17Cr​417−r2rr=1∑20​5r−119Cr−1​​ is equal to

4

6

9

18

r=0∑17​17Cr​417−r2rr=1∑20​5r−119Cr−1​​=r=0∑17​17Cr​417−r2rr=1∑20​5r−1⋅120−r⋅19Cr−1​​=617619​=36 Total number of factor of 36 is 9

Q. The number of divisors of the number $\frac{r = 1 \sum 20 5 ^{r - 1} ^{19} C _{r - 1}}{r = 0 \sum 17 ^{17} C _{r} 4 ^{17 - r} 2 ^{r}}$ is equal to

$\frac{r = 1 \sum 20 5 ^{r - 1} ^{19} C _{r - 1}}{r = 0 \sum 17 ^{17} C _{r} 4 ^{17 - r} 2 ^{r}} = \frac{r = 1 \sum 20 5 ^{r - 1} \cdot 1 ^{20 - r} \cdot ^{19} C _{r - 1}}{r = 0 \sum 17 ^{17} C _{r} 4 ^{17 - r} 2 ^{r}} = \frac{6 ^{19}}{6 ^{17}} = 36$
Total number of factor of 36 is 9