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# cheatsheet3 - Determine whether the statement is true or...

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Unformatted text preview: Determine whether the statement is true or false. If it is false: rewrite it as a true statement. If two events are mutually exclusive. they have no outcomes in common. Choose the correct answer helow. {jar-r. False. If two events are mutually exclusive: they have every outcome in common. -:j:j:- B. False. If two events are mutually exclusive. they have some outcomes in common. :35!" I2. True. Determine whether the statement is true or false. If it is false: rewrite it as a true statement. If two events are mutually exclusive, they have no outcomes in common. Choose the correct answer helow. {jar—r. False. If two events are mutually exclusive. they have every outcome in common. C:- B. False. If two events are mutually exclusin they have some outcomes in common. {55" I2. True. When you calculate the number of permutations of n distinct objects talren r at a time. what are you counting? Choose the correct answer helow. (go. The number of ordered arrangements of H objects talren r at a time. Evaluate the given expression and express the result using the usual format for writing numbers {instead of scientiﬁc notation). lﬂcd n! H C :— n ‘ {n-rjdr! Now, use the formula to find the value of the combination. Begin by substituting the correct numbers in the combination formula. c _ so: 3” ‘— (so—4M4! Evaluate the subtraction in the denominator. c _ so! 3” 4— 1+5! «1! Expand the factorial symbols and cancel the factors that the denominator and numerator share. a _2o-19-rs-rr-wt melt M.4.3.2.1 Further simpliﬁj the expression and carrj.r out the resulting product. This is the value of the combination. 10% = 4345 Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways 13 people can line up in a row for concert tickets. Does the situation involve permutations, combinations, or neither? Choose the correct answer below. ail-A. Neither. A line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects. {:1- B. Combinations. The order of the 13 people in line does not matter. 51.3.!“ I2. Permutations. The order of the 13 people in line matters. How man},r different lﬂI—letter words {real or imaginary) can be formed ﬁ'om the following letters? EL,RT,L,ZL,V,L,L a. .. rmu—L-ll—Luvu v... uvuwuﬂul .nm... .-.-.......-....... a. ur‘uumwl. a” u...- an...“ H... .-.- ”J .- .- vuJ-I—ru-u 5......- be arranged {order matters) in which there are 111 of one kind, nlofa second kind, and “1: of a lrth kind, where n :11] + “2+ + nk. The number of such permutations is given by the following formula. 11! nltnlt...nkt 1n the expression below the appropriate numbers have been substituted into the formula. Evaluate this expression to ﬁnd the number of ten-letter words {real or imaginary) that can be formed. It)! ll-Sl-ll-ll-ll-llzgﬂ’zw Therefore, 3ﬂ,Z4{} ten—letter words {real or imaginary) that can be formed with the letters above. Thepiecharttotherightshowshowadults rate their ﬁnancial shape. Suppose 4 people are chosen at random from a group of 1000. 1What is the probability that all four would rate their ﬁnancial shape as excellent? {Make the assmuption that 1000 the people are represented by the pie chart.) Thus, the possible muuber ot'ways of choosing 4 people from the group of 00 is soC4' The possible rnnuber of ways of choosing 4 people from the group of 1000 is 1011C 4. Using the classical probability formula, ﬁml the probability that all four would rate their ﬁnaudal shape as excellent. soc-1 P03) loose-1 431535 41,41 1124350 =5 0.000012 ...
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