A) i) if 4 individuals are selected from a group of 7 people, how many possible selection option could be made?

ii) in a competition prizes are given to 6 of the 10 participants. how many possible prize lists could be made if they are given different prizes?

b) in how many ways can the letters of the word semester be rearranged?

(a) 35 options

(b) 151,200 permutations

(c) 3,360 ways

Step-by-step explanation:

a) The number of combinations of p=4 people out of a n=7 can be calculated as

b) In this case is a permutation with no repetition of r=6 elements in a n=10 elements group.

c) The word semester has 2 S's, 3 E's, 1 M, 1 T and 1 R (8 letters in total).

The total amount of permutations can be calculated as the total amount of permutations of letters, divided by the factorial of the amount of times a same letter repeats in the word. Or is the same to say, dividing by the amount of repetitions of the same permutation.

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.