At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Let's evaluate the given expression step-by-step:
[tex]\[ \frac{{ }_8 C_3}{{ }_4 C_3}-\frac{811}{791} \][/tex]
1. Calculate [tex]\({ }_8 C_3\)[/tex]:
The combination formula is given by:
[tex]\[ { }_n C_r = \frac{n!}{r!(n-r)!} \][/tex]
Substituting [tex]\( n = 8 \)[/tex] and [tex]\( r = 3 \)[/tex], we get:
[tex]\[ { }_8 C_3 = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56 \][/tex]
2. Calculate [tex]\({ }_4 C_3\)[/tex]:
Substituting [tex]\( n = 4 \)[/tex] and [tex]\( r = 3 \)[/tex], we get:
[tex]\[ { }_4 C_3 = \frac{4!}{3!(4-3)!} = \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1 \times 1} = 4 \][/tex]
3. Evaluate the fraction [tex]\(\frac{{ }_8 C_3}{{ }_4 C_3}\)[/tex]:
[tex]\[ \frac{56}{4} = 14 \][/tex]
4. Evaluate the fraction [tex]\(\frac{811}{791}\)[/tex]:
The value of this fraction is approximately:
[tex]\[ \frac{811}{791} \approx 1.0253 \][/tex]
5. Subtract the two results:
[tex]\[ 14 - 1.0253 \approx 12.9747 \][/tex]
Therefore, the result of the expression
[tex]\[ \frac{{ }_8 C_3}{{ }_4 C_3} - \frac{811}{791} \][/tex]
is approximately:
[tex]\[ 12.9747 \][/tex]
[tex]\[ \frac{{ }_8 C_3}{{ }_4 C_3}-\frac{811}{791} \][/tex]
1. Calculate [tex]\({ }_8 C_3\)[/tex]:
The combination formula is given by:
[tex]\[ { }_n C_r = \frac{n!}{r!(n-r)!} \][/tex]
Substituting [tex]\( n = 8 \)[/tex] and [tex]\( r = 3 \)[/tex], we get:
[tex]\[ { }_8 C_3 = \frac{8!}{3!(8-3)!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56 \][/tex]
2. Calculate [tex]\({ }_4 C_3\)[/tex]:
Substituting [tex]\( n = 4 \)[/tex] and [tex]\( r = 3 \)[/tex], we get:
[tex]\[ { }_4 C_3 = \frac{4!}{3!(4-3)!} = \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1 \times 1} = 4 \][/tex]
3. Evaluate the fraction [tex]\(\frac{{ }_8 C_3}{{ }_4 C_3}\)[/tex]:
[tex]\[ \frac{56}{4} = 14 \][/tex]
4. Evaluate the fraction [tex]\(\frac{811}{791}\)[/tex]:
The value of this fraction is approximately:
[tex]\[ \frac{811}{791} \approx 1.0253 \][/tex]
5. Subtract the two results:
[tex]\[ 14 - 1.0253 \approx 12.9747 \][/tex]
Therefore, the result of the expression
[tex]\[ \frac{{ }_8 C_3}{{ }_4 C_3} - \frac{811}{791} \][/tex]
is approximately:
[tex]\[ 12.9747 \][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.