How many 4element DNA sequences Do not contain the base T Co

How many 4-element DNA sequences Do not contain the base T? Contain all four bases A, T, C and G? Contain exactly 2 of the four bases A, T, C, and G?

We are given 4-element DNA sequences

(a)

we know that there are four bases A , C , T and G

and bases can be repeated

so, if there is on T

it means that we have 3 bases with 4 places to arrange

so, number of ways that do not have base T = 3*3*3*3=3^4

number of ways that do not have base T=81.......Answer

(B)

we know that there are four letters

amnd there are four positions

It means that each letters will be exactly once used

so, number of ways of having all four bases A , T , C and G = 4*3*2*1

number of ways of having all four bases A , T , C and G=24...........Answer

(C)

we know that

There are 4 ways of choosing which base (A, C, G, or T) represents the pair

There are 4 choose 3 = 4 ways of choosing which 3 positions in the 4-element sequence are occupied by the pair

Once the pair has been established, there are 2 ways of choosing the base for the first of the remaining 2 unoccupied positions

2 ways of choosing the base for the remaining unoccupied position

so, we get

number of wyas = 4*3*2*2=48 ........Answer