Laura’s favorite clothes are five sweaters, four skirts, three jackets, two pairs of shoes and one belt. How many ways can Laura wear her favorite clothes without repeating the exact outfit?
she can pick 5 different sweaters, for each of those she can
pick 4 different skirts, for each of those she can pick
3 different jackets, for each of those........
number of ways = 5x3x3x2x1 =
To determine the number of ways Laura can wear her favorite clothes without repeating the exact outfit, we can use the concept of permutations.
First, let's calculate the total number of outfits Laura can create. Since Laura has 5 sweaters, 4 skirts, 3 jackets, 2 pairs of shoes, and 1 belt, the total number of outfits can be found by multiplying the numbers together: 5 * 4 * 3 * 2 * 1 = 120 outfits.
However, since Laura cannot repeat the exact outfit, we need to exclude the outfits where the same combination of clothes is repeated.
To calculate the outfits without the repetition, we need to find the number of permutations. A permutation is the arrangement of items in a particular order. In this case, we need to consider all possible arrangements of Laura's clothes without repetition.
To calculate the number of permutations, we can use the formula for permutation:
nPr = n! / (n - r)!
Where n is the total number of items (outfits) and r is the number of items selected (outfits worn).
In this case, we need to find the number of permutations of 120 outfits taken all at a time (n = 120, r = 120).
Plugging in these values into the formula, we have:
nPr = 120! / (120 - 120)!
= 120! / 0!
= 120!
Since 0! is equal to 1, the calculation becomes:
120! = 120 * 119 * 118 * ... * 3 * 2 * 1
= 6,689,502,913,449,127,774,686,924,929,666,408,945,758,881,051,019,354,752,000,000,000,000
Therefore, there are 6,689,502,913,449,127,774,686,924,929,666,408,945,758,881,051,019,354,752,000,000,000,000 ways for Laura to wear her favorite clothes without repeating the exact outfit.