NCERT Class XI Mathematics - Permutations and Combinations - Solutions
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Question : 20
Total: 41
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
Solution:
There are 11 letters, of which I appears 4 times, S appears 4 times, P appears 2 times & M appears 1 time.
∴ The required number of arrangements
=
= 11 × 10 × 9 × 7 × 5 = 34650 ... (i)
When four I’s come together, we treat them as a single object. This single object with 7 remaining objects will account for 8 objects. These 8 objects in which there are 4S’s & 2P’s can be rearranged in
Number of arrangements when four I’s do not come together
= 34650 – 840 = 33810.
∴ The required number of arrangements
=
= 11 × 10 × 9 × 7 × 5 = 34650 ... (i)
When four I’s come together, we treat them as a single object. This single object with 7 remaining objects will account for 8 objects. These 8 objects in which there are 4S’s & 2P’s can be rearranged in
Number of arrangements when four I’s do not come together
= 34650 – 840 = 33810.
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