Permutations and Combinations Test -8

We have 38808 = 2³3²7²11¹

To form factors we have to do selections from a lot of 2's,3's,7's and 11's and multiply them together.

Number of ways of selecting any number of 2's from a lot of 3 identical 2's=4(select 0,select 1,select 2,select 3)

Number of ways of selecting any number of 3's from a lot of 2 identical 3's=3(select 0,select 1,select 2)

Number of ways of selecting any number of 7's from a lot of 2 identical 7's=3(select 0,select 1,select 2)

Number of ways of selecting any number of 11's from a lot of 1 identical 11's=2(select 0,select 1)

Hence we get the total number of ways of selecting factors=4 × 3 × 3 × 2 = 72

Hence number of factors other than 1 and n = 72 − 2 = 70

We have to find the total number of four digit odd numbers formed using the digits 0,1,2,3,5,7

Since it is an odd number the last place ( unit's place) can be filled by any of the odd numbers 1,3,5,7 in 4 different ways.

Since repetition is allowed the second and third places can be filled by any of the six given digits

Since it has to be a four digit number  the first place can be filled by any of the five given digits other than zero in 5 ways

Hence all the four places can be filled in 4 × 6 × 6 × 5 = 720 ways

to make necklace, beads can be arranged in (n-1)! ways, also the clockwise and anticlockwise is same so we divide by 2!