Question

# The number of necklaces which can be formed by selecting 4 beads out of 6 beads of different coloured glasses and 4 beads out of 5 beads of different metal, is-

^{6}P_{4} × ^{5}P_{4 }×
^{6}C_{4} × ^{5}C_{4} ×
^{6}C_{4} × ^{5}C_{4} ×
^{6}C_{4} × ^{5}C_{4} × 7!

^{6}P_{4}×^{5}P_{4 }×^{6}C_{4}×^{5}C_{4}×^{6}C_{4}×^{5}C_{4}×^{6}C_{4}×^{5}C_{4}× 7!Hint:

### If the necklace on the left is turned over, we obtain the arrangement on the right, i.e., anticlockwise and clockwise order of arrangement is not different.

Already, we know that the number of circular permutations when anticlockwise and clockwise order of arrangement is different as (n-1)!

Hence the number of arrangement of the necklace with beads =

## The correct answer is: ^{6}C_{4} × ^{5}C_{4} ×

### In all we are using 8 beads to form a necklace,

Number of ways necklaces can be formed by selecting 4 beads out of 6 beads of different coloured glasses =

Number of ways necklaces can be formed by selecting 4 beads out of 5 beads of different metal =

If the necklace on the left is turned over, we obtain the arrangement on the right, i.e., anticlockwise and clockwise order of arrangement is not different.

Hence the number of arrangement of the necklace with beads =

Total number of necklaces = × ×

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