Damn you, Mendel!

Number Theory Level 3

What you need to know -

Human have 1 pair of sex chromosome & 22 pairs of autosomes (not sex chromosome) .
Allele refers to placement of single chromosome of any pair.
Every autosome has a dominant allele which gets to determine appearance of an individual & a recessive allele which doesn't get to do that !
When a baby is born, one chromosome is from father & the other chromosome is from mother .
And in case of sex chromosome, you are either a man (XY) or a woman (XX) .

The question is, how many baby of different chromosomes can be born from a father & a mother in 1st generation if every allele is different ?

23C_2

2^{23}

23P_2

can NOT be determined

4^{23}

2 \times 4^{22}

1 solution

Moaj Ahmed
Nov 6, 2017

suppose, for pair of chromosome no. 1 , father has ( $a_1$ $b_1$ ) & mother has ( $c_1$ $d_1$ ) , so baby can have ( $a_1$ $c_1$ ) or ( $a_1$ $d_1$ ) or ( $b_1$ $c_1$ ) or ( $b_1$ $d_1$ ) → 4 possible outcome for chromosome pair no. 1

this is same for the 22 pair of autosomes !

for the sex chromosome, only 2 outcome is possible

so, by the rule of product , the answer is $2 \times 4^{22}$

Damn you, Mendel!

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