four seniors and six juniors are competing for four places on a quiz bowl team. what is the approximate…

Explanation:

Step1: Calculate total number of students

There are 4 seniors and 6 juniors, so the total number of students is $4 + 6=10$.

Step2: Calculate number of ways to choose 4 students out of 10

We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 10$ and $r = 4$. So $C(10,4)=\frac{10!}{4!(10 - 4)!}=\frac{10\times9\times8\times7}{4\times3\times2\times1}=210$.

Step3: Calculate number of ways to choose 4 seniors out of 4

Using the combination formula with $n = 4$ and $r = 4$, $C(4,4)=\frac{4!}{4!(4 - 4)!}=1$.

Step4: Calculate the probability

The probability $P$ that all four - seniors are chosen is the number of favorable outcomes (choosing 4 seniors) divided by the number of total outcomes (choosing 4 students out of 10). So $P=\frac{C(4,4)}{C(10,4)}=\frac{1}{210}\approx0.00476$.

Answer:

0.00476