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Quantitative Aptitude

Combination

Suppose the u...

Question

Suppose the union of sets S1 and S2 is X and S1, S2 have the same number of elements. If elements S1, S2 are chosen randomly it was found that by exchanging two elements of S1 with two elements of S2, every element of S1 was greater than that of S2. Find the no. of sets S1 that can be formed.

$^{50} C_{2}$

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$^{50} C_{49}$

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$100$

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$^{50} C_{49} \times^{50} C_{2}$

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Solution

The correct option is D
$^{50} C_{49} \times^{50} C_{2}$

In set S1, 48 elements can be selected randomly in $^{50} C_{48}$ ways (from 51 to 100) and the other two elements in S1 can be selected in $^{50} C_{2}$ ways (from 1 to 50). So, set S1 can be formed in $^{50} C_{48} \times^{50} C_{2}$ ways. Hence option (d) is correct.

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Suppose the union of sets S1 and S2 is X and S1, S2 have the same number of elements. If elements S1, S2 are chosen randomly it was found that by exchanging two elements of S1 with two elements of S2, every element of S1 was greater than that of S2. Find the no. of sets S1 that can be formed.

The correct option is D 50C49×50C2 In set S1, 48 elements can be selected randomly in 50C48 ways (from 51 to 100) and the other two elements in S1 can be selected in 50C2 ways (from 1 to 50). So, set S1 can be formed in 50C48×50C2 ways. Hence option (d) is correct.