How does the random alignment of homologous chromosomes during metaphase i contribute to the variation in cells produced by meiosis?

The variation in cells produced by meiosis occurs because of crossing over that takes place during pachytene, a substage of Prophase I.

Explanation:

Meiosis I is consist of four stages Propase I, Metaphase I, Anaphase I and Telophase I.

Prophase I of Meiosis I has five substages namely; Leptotene, Zygotene, Pachytene, Diplotene and Diakinesis.

Leptotene. Each chromosomes has two long threads of sister chromatids as result of replication during the S phase of the cycle.

Zygotene. The pairing of chromosomes begin. Pair of chromosomes are called homologous chromosomes.

Pachytene. Chromosomes are thick due to repeated coiling. Crossing over takes place during this stage where a segment of sister chromatid of one chromosome is exchange with the same segment of the sister chromatid of the homologous chromosomes through the formation of a cross-linkage of the segments called chiasma. After crossing over, the sister chromatids of each chromosome is no longer identical with each other based on the genetic material that they contain. This is the very reason why there is variation in the cells produce by meiosis ...

During metaphase, paired chromosomes simply align themselves at the equatorial plate.