F.5permutation and combination

2010-11-24 3:09 am

1) Find the no. of ways of forming a 6-digit number with different digits by using the ten numerals 0 to 9.
ans:136 080

2) There are 10 successive parking spaces in a car park. 7 cars are going to park in these places. If it is required that 3 unoccupied spaces are next to each other,in how many ways can the spaces be assigned to the cars?
ans: 40 320

3) Five letters are taken from the word " HISTORAM " and arranged. FInd
the no. of ways of arranging them if
a)the last letter is a vowel
b)the first and the last letters are consonants.
ans: a)5040
b)6300

pls show clear steps.thx!

回答 (1)

用戶9112

2010-11-24 6:13 am

✔ 最佳答案

(1) The first digit cannot be 0 so have 9 waysSecond digit is different from the first =9 waysThird digit 8 ways, fourth 7 ways , fifth 6 and last digit 5In total 9×9×8×7×6×5=136080 ways(2)Consider the 3 unoccupied spaces as one unit.Arranging this unit with the other 7 spaces, there are8!=40320 ways to arrange them(3)(a)I think the question should be HISTOGRAMChoose the last letter C(3,1)=3waysPick the remaining 4 from among 8 and considering the arrangementsThere are P(8,4)=1680 waysTotal number of ways=3×1680=5040 ways(b)First pick the first and last letters from among 6 with arrangement order=P(6,2)=30 waysPick the rest 3 from among 7 with arrangement=P(7,3)=210 waysIn total 30×210=6300 ways

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