To determine the value of [tex]\( n \)[/tex] in the equation [tex]\( 7! + 8! + 9! = n \times 6! \)[/tex], let's follow a step-by-step approach:
1. Calculate each of the factorials involved:
- [tex]\( 6! \)[/tex] which equals 720.
- [tex]\( 7! \)[/tex] which equals 5040.
- [tex]\( 8! \)[/tex] which equals 40320.
- [tex]\( 9! \)[/tex] which equals 362880.
2. Sum the factorials:
[tex]\[
7! + 8! + 9! = 5040 + 40320 + 362880 = 408240
\][/tex]
3. Substitute these values into the equation:
[tex]\[
408240 = n \times 720
\][/tex]
4. Solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{408240}{720} = 567
\][/tex]
Thus, the value of [tex]\( n \)[/tex] is [tex]\( 567 \)[/tex]. Given the choices, the correct one corresponding to this value is not listed among A, B, C, D, or E. So, the value of [tex]\( n \)[/tex] is actually a different value than those provided in the question options.
