Question

Please answer I’ll rate brainlyest

Answer 1

Answer:

$5P3*6C4=60*15=900$

Step-by-step explanation:

$5P3$ refers to the permutations of 5 items taken 3 at a time. To evaluate this, we use factorials as follows;

$5P3=\frac{5!}{(5-3)!}$

The factorial of an integer n is evaluated as;

$n!=n*(n-1)*(n-2)*(n-3).......3*2*1$

Using this concept, the above expression can now be simplified as follows;

$5P3=\frac{5!}{2!}=\frac{5*4*3*2!}{2!}=5*4*3=60$

Therefore, the permutations of 5 items taken 3 at a time is 60.

The next expression, $6C4$ refers to the combinations of 6 items taken 4 at a time. The simplification utilizes similar concepts of permutations since we shall be involving factorials;

$6C4=\frac{6!}{4!(6-4)!}=\frac{6!}{4!*2!}=\frac{6*5*4!}{4!*2*1}=\frac{6*5}{2*1}=15$

Therefore, the combinations of 6 items taken 4 at a time is 15.

The final step is to evaluate the product;

$5P3*6C4=60*15=900$