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 ways to choose 4 students

The total number of students is (4 + 6=10). The number of ways to choose 4 students out of 10 is given by 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).

Step2: Calculate number of ways to choose 4 seniors

There are 4 seniors, and the number of ways to choose 4 seniors out of 4 is (C(4,4)=\frac{4!}{4!(4 - 4)!}=1).

Step3: Calculate the probability

The probability (P) that all 4 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