Perform the indicated calculation. $$ { }_{42} P_{2} $$ $$ { }_{42} P_{2}=\square $$ (Type a whole number.)

Question

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Solution:
  $$\frac{42!}{\left(42-2\right)!}$$
- step1: Subtract the numbers:
  $$\frac{42!}{40!}$$
- step2: Expand the expression:
  $$\frac{42\times 41\times 40!}{40!}$$
- step3: Reduce the fraction:
  $$42\times 41$$
- step4: Multiply the numbers:
  $$1722$$
The calculation for $$ { }_{42} P_{2} $$ is given by the formula:

$$
{ }_{n} P_{r} = \frac{n!}{(n-r)!}
$$

For $$ n = 42 $$ and $$ r = 2 $$:

$$
{ }_{42} P_{2} = \frac{42!}{(42-2)!} = \frac{42!}{40!}
$$

This simplifies to:

$$
42 \times 41 = 1722
$$

Thus, $$ { }_{42} P_{2} = 1722 $$.
$$ { }_{42} P_{2} = 1722 $$

Perform the indicated calculation. \( { }_{42} P_{2} \) \( { }_{42} P_{2}=\square \) (Type a whole number.)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Probability Questions