Respuesta :
Answer:
There are 1,039,584 ways in which this can be done.
Step-by-step explanation:
Total number of black marbles = 17
Total number of blue marbles = 9
The number black marbles to be chosen = 6
The number blue marbles to be chosen = 3
So, we have to choose 6 black from 17 black marbles.
and to choose 3 blue from 9 blue marbles.
So, the number if possible ways to do it : [tex]^{17} \textrm{C}_ {6} \times ^{9} \textrm{C}_ {3}[/tex]
[tex]^{n} \textrm{C}_ {r} = \frac{n! }{r! (n-r)!}[/tex]
Now, solving [tex]^{17} \textrm{C}_ {6}[/tex], we get:
[tex]^{17} \textrm{C}_ {6} = \frac{17!}{6! \times 11!} \\= \frac{17 \times 16 \times 15 \times 14\times 13\times 12 \times 11! }{11! \times (6\times 5 \times 4 \times 3\times 2)} = 12,376[/tex]
solving [tex]^{9} \textrm{C}_ {3}[/tex], we get:
[tex]^{9}\textrm{C}_{3} = \frac{9!}{6! \times 3!}\\= \frac{9 \times 8 \times 7 \times 6! }{6!\times (3\times 2 )} = 84[/tex]
[tex]\implies^{17}\textrm{C}_ {6}\times ^{9} \textrm{C}_ {3}=12,376 \times 84 = 1,039,584[/tex]
Hence, there are 1,039,584 ways in which this can be done.
