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F.5permutation and combination
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 0802) 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... 顯示更多 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!
最佳解答:
(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
其他解答:4E350C6F8B48ECA2
F.5permutation and combination
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發問: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 0802) 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... 顯示更多 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!
最佳解答:
(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
其他解答:4E350C6F8B48ECA2
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