Question

The letters G, E, N, I, D, S are placed in a bag. What is the probability that the letters are randomly pulled from the bag in the order that spells DESIGN?

Answer 1

Answer as a fraction = 1/5040

Answer in decimal form (approximate) = 0.000198

Answer in percentage form (approximate) = 0.0198%

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Explanation:

There is only one ordering of the letters to get DESIGN out of 5040 different permutations. The 5040 comes from the fact that 7*6*5*4*3*2*1 = 5040. In shorthand notation, use factorials to say 7! = 5040. Notice how we started with 7 and counted down until reaching 1, multiplying all along the way. You could use the nPr permutation formula to get the same result of 5040 (use n = 7 and r = 7).

So because we have 1 way to order the letters (getting DESIGN) out of 5040 ways total, this means the probability is the fraction 1/5040. Use your calculator to find that 1/5040 = 0.000198 approximately. Move the decimal over 2 spots to the right to convert 0.000198 to 0.0198%