Additional Concepts
-$\frac { { } _ { 7 } C _ { 3 } } { { } _ { 5 } C _ { 1 } } - \frac { 48 ! } { 46 ! }$
A) $- 2249$
B) 2249
C) $- 2345$
D) $- 41$

Question

Quizplus · Accepted Answer

The expression simplifies as follows: $\frac { { } _ { 7 } C _ { 3 } } { { } _ { 5 } C _ { 1 } } - \frac { 48 ! } { 46 ! }$ can be simplified step by step. First, calculate the combinations and the factorial fractions:${ } _ { 7 } C _ { 3 } = \frac{7!}{3!(7-3)!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$${ } _ { 5 } C _ { 1 } = \frac{5!}{1!(5-1)!} = \frac{5}{1} = 5$So, the first part of the expression becomes $\frac{35}{5} = 7$.For the second part:$\frac { 48 ! } { 46 ! } = \frac{48 \times 47 \times 46!}{46!} = 48 \times 47 = 2256$Putting it all together:$7 - 2256 = -2249$

Additional Concepts - 7C35C1−48!46!\frac { { } _ { 7 } C _ { 3 } } { { } _ { 5 } C _ { 1 } } - \frac { 48 ! } { 46 ! }5​C1​7​C3​​−46!48!​

Additional Concepts
- $\frac { { } _ { 7 } C _ { 3 } } { { } _ { 5 } C _ { 1 } } - \frac { 48 ! } { 46 ! }$