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UPSC Prelims

Mathematics

Theme:

Permutation and Combination / क्रमचय और संचय

Q72 2016, Permutation and Combination

Four-digit numbers are to be formed using the digits 1, 2, 3, and 4; and none of these four digits are repeated in any manner. Further,
1. 2 and 3 are not to immediately follow each other
2. 1 is not to be immediately followed by 3
3. 4 is not to appear at the last place
4. 1 is not to appear at the first place
How many different numbers can be formed?

अंक 1, 2, 3 और 4 को लेकर चार-अंकीय संख्याएं बतानी हैं। इन चार अंकों में से किसी एक की भी किसी भी रीति से पुनरावृत्ति नहीं करनी है, तथा
1. 1, 2 और 3 एक दूसरे के एकदम आगे पीछे नहीं हो सकते
2. 3, 1 के एकदम पीछे नहीं हो सकता
3. 4 अंतिम स्थान पर नहीं आ सकता
4. 1 प्रथम स्थान पर नहीं आ सकता
कितनी पृथक संख्याएं बन सकती हैं?

Explanation Please wait..

From the given conditions, for the four positions available :

1 cannot come at the first place. So 2, 3 and 4 can appear there.

4 cannot come at the last place. So 1, 2 and 3 can appear there.

2 and 3 cannot immediately follow each other. So 23 and 32 is not allowed.

1 cannot be immediately followed by 3. So 13 is not allowed.

Let us list the possible numbers now -

2431 --- possible, does not violate any condition

2143 --- possible, does not violate any condition

3142 --- possible, does not violate any condition

3412 --- possible, does not violate any condition

3421 --- possible, does not violate any condition

4312 --- possible, does not violate any condition

Hence, answer is (a). Total 6 numbers are possible.

व्याख्या Please wait..

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