If a die is rolled 40 times, there are 640 different sequences possible. the following question asks how many of these sequences satisfy certain conditions. hint [use the decision algorithm discussed in example 3 of section 6.3.] what fraction of these sequences have exactly five 1s? (round your answer to four decimal places.)

0.1433

Step-by-step explanation:

The total number of different sequences in 40 rolls of a die is

                         The 1s may occur at any 5 rolls among 40. The number of ways of exactly five 1s occuring is therefore, equivalent to number of ways of selecting 5 fruits from 40 distinct fruits which is ⁴⁰C₅ ways. These 5 rolls have a fixed outcome 1. Other 35 rolls each have 5 possible outcomes : 2 or 3 or 4 or 5 or 6. So, the number of possible sequences of outcomes on other 35 rolls of the die is .

⇒The total number of different sequences having exactly five 1s in 40 rolls of a die is (⁴⁰C₅)×()

∴The fraction of the total number of sequences having exactly five 1s is )}{}" alt="5^{35}" />)}{}" /> ≈ 0.1433

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

answ5

step-by-step explanation:

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