SOLUTION: 1) A grocery store makes up fruit baskets using as many as four apples, three peras, adn for oranges. A basket must contain at least on piece of fruit. How many different fruit sel

Question 27044: 1) A grocery store makes up fruit baskets using as many as four apples, three peras, adn for oranges. A basket must contain at least on piece of fruit. How many different fruit selections are possible?
2)A 10-letter word consists of 4 A's and 6 B's. HOw many different words are possible if no two A's can be next to eachother? (hint start with BBBBBB and decide where to put the A's)
3) A computer manufacturer has 50 distinct microchips to place into a rectangular array that is 5 units wide by 10 units long:
a)In how many ways can the chips be arranged?
b)Ten of the chips control special functions. How many arrangements are possible if these occupy the 1st column
c) Find the number of arrangements having no special-function chips in the 1st column.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
1) A grocery store makes up fruit baskets using as many as four apples, three peras, adn for oranges. A basket must contain at least on piece of fruit. How many different fruit selections are possible?
APPLES...WE MAY SELECT...0.. OR.. 1.. OR... 2... OR...3.. OR... 4 ..=.5 WAYS
PEARS...WE MAY SELECT...0.. OR.. 1.. OR... 2... OR...3.. ...........=4 WAYS
ORANGES...WE MAY SELECT...0.. OR.. 1.. OR... 2... OR...3.. OR... 4 ..=5 WAYS
NUMBER OF DIFFERENT POSSIBILITIES=5*4*5=100 WAYS..BUT THIS INCLUDES SELECTING ONE WAY OF SELECTING ZERO FROM EACH TYPE OR NONE WHICH IS NOT ALLOWED
SO NUMBER OF POSSIBILITIES =100-1=99

2)A 10-letter word consists of 4 A's and 6 B's. HOw many different words are possible if no two A's can be next to eachother? (hint start with BBBBBB and decide where to put the A's)
6 B'S CAN BE ARRANGED IN 6!/6!=1 WAY AS THEY ARE ALL SAME.WE CAN INSERT A'S IN 2 ENDS AND 5 GAPS BETWEEN B'S AS TWO A' CANNOT BE TOGETHER.THAT IS THERE ARE 7 POSITIONS
NUMBER OF WAYS =7!/4!
HENCE NUMBER OF DIFFERENT POSSIBILITIES ARE 1*7!/4!=7*6*5=210
3) A computer manufacturer has 50 distinct microchips to place into a rectangular array that is 5 units wide by 10 units long:
a)In how many ways can the chips be arranged?
THERE ARE 5*10=50 SQUARES..SO 50 CHIPS CAN BE ARRANGED IN 50 SQUARES IN 50! WAYS
b)Ten of the chips control special functions. How many arrangements are possible if these occupy the 1st column
TOP 10 POSITIONS FOR 10 SPECIAL BUT DISTINCT CHIPS CAN BE ARRANGED IN 10! WAYS
REST 40 IN 40 PLACES CAN BE ARRANGED IN 40! WAYS
HENCE TOTAL NUMBER OF POSSIBILITIES =10!*40!
c) Find the number of arrangements having no special-function chips in the 1st column.
10 SPECIAL CHIPS CAN BE ARRANGED IN 40 SQUARES IN 40P10 WAYS =40!/(40-10)=40!/30! WAYS.
REST 40 IN REMAINING 40 PLACES IN 40! WAYS.
HENCE TOTAL =40!*40!/30!

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