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Hello everyone.
00:01
So this is the question that we have part a.
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We need to tell how many permutations how many permutations be belonging to s6 satisfy p to the part 3 id where id is equal to 1, 2, 3, 4, 5, 6 which is the identity permutation.
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Part b, that how many, e, even permutations are there which satisfy p belonging to s6, p to b to be par 3 is equal to i .d.
00:46
So let's jump onto the solution of the question.
00:50
This is the condition that we have for part a.
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Pq is equal to identity permutation d.
00:59
So modulus of p would be equal to 3, which will be 1 .3.
01:06
Three so if we look at the order number of elements number of elements of order three are gonna be a one it is gonna be one divided by three six factorial divided by six minus three factorial which is going to be one divided by three six factorial divided by three six factorial divided by three so this is going to be equal to nothing but 40 equal to 40 now if we look for the number of elements so on simplifying further for these order for a 1 a 2 a 3 we have done now for number of elements of order 3 a 1 a 2 a 3 a 2 a 3 a 4 a 5 and 8 6 so this is going to be half multiplied by 1 divided by 3, 6 factorial divided by 6 minus 3 factorial multiplied by 1 divided by 3, 3 factorial divided by 3 minus 3 factorial...