It is more likely to draw a royal flush from a deck of 52 cards if the cards can be drawn in any order. In this case the first card is 20/52 because there are four suits (club, spade, heart & diamond) and five different cards (ace, king, queen, jack & ten) to choose from. Then you must consider all the possible orders (permutations) that the cards can be drawn, such as ace-king-queen-jack-ten, ten-jack-queen-king-ace, ace-jack-ten-king-queen, etc. The number of permutations can be calculated from five factorial or 5! = 5 X 4 X 3 X 2 X 1 = 120:

According to B. Siskin and J. Staller (What are the Chances?, Crown Publishers, Inc., New York, 1989), the chance of being struck by lightning in your lifetime is one in 600,000. Compare this with the chance of winning the state lottery (one in 23 million)! Of course, the chance of being struck by lightning is increased significantly if you stand on a barren mountain summit (above timberline) holding a metal rod during a thunder storm.

The male (XY) and female (XX) offspring in the above table are in a 50-50 ratio with an equal number of boys and girls. Therefore, the chance of having a boy is 1/2 or 50% and the chance of a girl is also 1/2 or 50%. This ratio can be demonstrated by tossing a coin many times and keeping track of the number of heads and tails. If enough tosses are made, the number of heads and tails should be very close to 50-50.

Unfortunately in biology, sex ratios in humans are not that easily explained. In the United States, there is a slightly better chance of having a boy, about 105 males to 100 females. There are a number of hypotheses (tentative explanations) for this unequal birth ratio, most of which are probably not accurate. If this unequal birth ratio is the result of a greater number of male conceptions, then perhaps the Y-sperm has a slightly better advantage in reaching the egg or penetrating the barrier of follicle cells around the egg, possibly by the smaller size of its head and faster speed. According to some references, muscular contractions and ciliary currents within the female reproductive tract are primarily responsible for transporting the sperm to the egg. In vitro, sperm can swim about 3 mm per minute, but within the vagina and oviduct (in vivo) they can travel about 5 mm per minute. Since the speed is additive, a faster Y-sperm could potentially still win the race to the egg. It has been demonstrated that Y-bearing sperm do not live as long as X-bearing sperm, so the time of ovulation and sexual intercourse could be a factor in determining the sex of a child. By the time the sperm reach the upper part of the fallopian tube where fertilization occurs, most of the Y-sperm may have already died. In this case when the egg is released from the ovary, the odds would be favor fertilization by an X-bearing sperm resulting in a girl. Another hypothesis for unequal sex ratios is an unequal number of X-bearing and Y-bearing sperm in the man's semen. Some references state that this condition might be hereditary, but it is not clearly explained in more scholarly texts.

A more plausible explanation for unequal birth ratios may involve the rejection of an embryo by the mother's antibodies. Conceptions may be approximately equal, but a greater loss of female embryos early in the gestation period may account for slightly more male births. The mother has two X-chromosomes, one from her mother and one from her father. Perhaps the X-chromosome from her father carries a gene that sensitizes her against the female fetus. In other words she develops antibodies against proteins of the female fetus but not the male fetus. Remember that these are only hypotheses at this time and should not be accepted as the final answer. When more testing is done, perhaps one or more of these hypotheses will become a widely-accepted theory.

Instant Insanity: 4 cubes whose faces (sides) have 4 colors (red, green, blue & white). The object is to stack cubes so that all 4 colors show on each side of stack. Each cube can be arranged in 24 different positions (6 sides x 4 colors = 24). The number of possible arrangements is 244 = 331, 776; however, the solved puzzle has multiple valid orientations so you must divide 331,776 by the number of valid orientations. See folowing: According to Wikipedia, the solution is symmetrical 8 ways: If you have a solution, and you flip all of the cubes forward, you have another valid solution. You can do that move 4 times. You can also rotate each cube 180 degrees around its vertical axis, which gives 2 more possiblities, a total of 4 x 2 = 8. Therefore, the total number of arrangements (244) must be divided by 8. NOTE: As of 22 March 2023, I question previous calculation. See next paragraph with blue background: After carefully examining my puzzle and the rules for puzzle solution, I am convinced there are 24 configurations for a vertical stack of 4 cubes, each side with 4 colors as specified in the rules. Each configuration can be rotated 4 times to verify the colors. If you randomly reshuffle the 4 cubes, you may get another stack with a different order of colors that counts as another solution, as long as all 4 sides have all 4 colors. Therefore, if you divide the total number of arrangements (244) by 24, the chance of getting a correct solution is 1/13,824. This is a little more like likely than 1/331,776!