Evaluate the expression. \( { }_{7} \mathrm{P}_{4} \) The solution is \( \square \).

To evaluate the expression \( { }_{7} \mathrm{P}_{4} \), we use the formula for permutations, which is given by: \[ {}_{n}P_{r} = \frac{n!}{(n-r)!} \] In this case, \( n = 7 \) and \( r = 4 \). Plugging in the values, we get: \[ {}_{7}P_{4} = \frac{7!}{(7-4)!} = \frac{7!}{3!} \] Now, calculate \( 7! \) and \( 3! \): \[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 \] \[ 3! = 3 \times 2 \times 1 = 6 \] Now substitute these values back into our equation: \[ {}_{7}P_{4} = \frac{5040}{6} = 840 \] So, the solution is \( 840 \).