# We can find the value of n by solving the equation 1

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We can find the value of n by solving the equation 1 (0 . 9) n = 0 . 95: n = log0 . 05 log0 . 90 29 . 8. How many different ways are there of putting the spots on a die? Answer: There are two sets of axes in 3-space: the clockwise and the anti- clockwise. We can imagine fixing the numbers to the vertices of these axes. Therefore the basic question is how many different ways are there of pairing 6 objects. Let us begin with the permutation of 6 objects : 6! Each permutation implies a set of pairs if we take the ordered elements two-by-two. Within each permutation the ordering of the pairs does not matter, so we must divide the number of permutation by 3!. Nor does the order of precedence within the pairs matter, so we must divide again by 2 3 . The number which we derive is 6! 3!2 3 = 15 . But, if we recall that there are two sets of axes, then we see that the total number of ways of fixing the spots on a die is 30. 3
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