In a diploid organism with 2n=8, what is the probability that one of its gametes will contain only paternally derived chromosomes (ie, not a mixture of paternal and maternally derived chromosomes)?

Since 4 of the 8 are paternal,

4/8 * 3/7 * 2/6 * 1/5 = ?

can you please explain how you got those numbers.

To find the probability that one of the gametes in a diploid organism will contain only paternally derived chromosomes, we first need to determine the total number of possible gametes and then the number of gametes that meet the specific criteria.

In a diploid organism, the number of chromosomes is represented as 2n, where n is the number of different types of chromosomes. In this case, 2n is given as 8, which means there are a total of 8 chromosomes.

Since the organism is diploid, it has two sets of chromosomes—one set from the mother and one set from the father. Therefore, it has 4 paternal (paternal-derived) chromosomes and 4 maternal (maternally derived) chromosomes.

To calculate the total number of possible gametes, we need to use the formula 2^n, where n represents the number of different types of chromosomes. In this case, there are 2 types of chromosomes (paternal and maternal), so the total number of possible gametes is 2^2 = 4.

Now we need to determine how many of those gametes contain only paternally derived chromosomes. Since there are 4 paternal chromosomes and no mixing is allowed, each gamete must inherit all 4 paternal chromosomes.

Therefore, there is only 1 possible gamete that meets the criteria of containing only paternally derived chromosomes.

To find the probability, we divide the number of favorable outcomes (gametes with paternally derived chromosomes only) by the total number of possible outcomes (total number of gametes).

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Probability = 1 / 4

So, the probability that one of the gametes in a diploid organism with 2n = 8 will contain only paternally derived chromosomes is 1/4.