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khyati

pls. answer the questions.....((ACTUALLY I NEED DETAILED SOLUTIONS )).

1. Find the number of students to be selected at a time from a group of 14 students so that the number of selections is greatest.Find the greatest number of selections.Also find the greatest number of selections when there are 15 students .

2. 5 points are given on one of the 2 parallel straight lines & 10 points are given on the other straight line. how many triangles can be formed by taking these points as vertices of a triangle ?

3.how many different numbers of 4 digits each ( without repetition of digits ) can be formed withthe digits 0,1,2,3,4,5,6 so that the digits in each number are in

a. descending order

b. ascending order

anyway ...... pls.. repy to this at least

ARE SUCH TOUGH QUESTIONS LIKELY TO COME FOR IIT ??

&&thnks in advance ,.......

HIMANSHU JAIN

1) greatest no. of selection is for mid value,i.e., 7 here.

no. of sel. = 14C₇

for 15, it is 15C₈or 15C₇ (both r same)

2) we can choose two pts. on one line&

one on other.

:. we get

5C₂ 10C₁ + 5C₁10C₂ = 325

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gaurav arora

3) a out of 0,1,2,3,4,5,6
no.of ways of selecting four digits is 7C4
These four no.selected can be arranged in decreasing order in only one way
So the answer is 7C4=35

gaurav arora

In the b part the no.of cases in which 0 is there are not possible as it cannot be in the first place
The answer is 6C4=15

Bipin Dubey

When n is even, ⁿC_r is maximum for r = n/2

When n is odd, ⁿC_r is maximum for r = (n+1)/2 or r = (n-1)/2

When 14 students are there (n is even) :
Greatest number of selections is for r = n/2 = 14/2 = 7
Greatest number of selections = ¹⁴C₇

When 15 students are there (n is odd) :
Greatest number of selections is for r = (n+1)/2 = 8 or (n-1)/2 = 7
Greatest number of selections = ¹⁵C₇ = ¹⁵C₈

geethu

Q3:

no:of ways 2 choose any 4 no: = 7C4 =35

only way 2 arrange any 4 no: in asending or desending order

no: cant start with 0

nos starting with 0 = 35/7 =5(out of 35 5 each start with any digit among d given 7)

req nos = 35-5 = 30

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